List of Published Papers by Goo Ishikawa

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Papers with Refereeing

[68] Goo Ishikawa, Singularities of parallels to tangent developable surfaces,
Tohoku Mathematical Journal, vol.75-2, (2023), 233--249.
DOI: 10.2748/tmj.20211220
(accepted on 20 December 2021.)
arXiv version

[67] Goo Ishikawa and Stanislaw Janeczko, Symplectic singularities of differentiable mappings,
in Differential geometry, Calabi-Yau theory, and general relativity,
Lectures and articles celebrating the 70th birthday of Shing Tung Yau,
Surveys in Differential Geometry, Volume 24-II, published in 2021. International Press, pp. 117--172.

[66] Goo Ishikawa, Normal and tangent maps to frontals,
Journal of Mathematical Sciences, Vol. 255, No. 5 (2021), 664--677.
DOI: https://doi.org/10.1007/s10958-021-05403-5
(accepted on 13 December 2020.)
arXiv version

[65] Goo Ishikawa, Motoki Oyama, Topology of complements to real affine space line arrangements,
Journal of Singularities, volume 22 (2020), 373-384
(accepted on 14 October 2020. )
Published version

[64] G. Ishikawa, S. Janeczko, Singular mappings and their zero-forms,
Pure and Applied Mathematics Quarterly, Volume 16, Number 5, (2020) 1643--1657.
(accepted on 26 February 2020. )
The first draft
The final draft before publication

[63] Goo Ishikawa, Recognition Problem of Frontal Singularities,
Journal of Singularities, vol.21 (2020), 149--166.
volume
The first draft (v2): arXiv:1808.09594 [math.DG]
The revised draft with figures, 2020.1.22-version.

[62] Goo Ishikawa, Yumiko Kitagawa, Asahi Tsuchida, Wataru Yukuno, Duality of (2,3,5)-distributions and Lagrangian cone structures,
Nagoya Mathematical Journal. Published online by Cambridge University Press: 23 January 2020, pp. 1-13.
DOI: https://doi.org/10.1017/nmj.2019.46
(accepted on 27 Nov. 2019).
The first draft: arXiv:1808.00149 [math.DG]

[61] Goo Ishikawa, Cofrontals,
REVUE ROUMAINE DE MATH{\' E}MATIQUES PURES ET APPLIQU{\' E}ES, Vol. 60--4 (2019), 461--478.
Proceedings of Australian-Japanese Real and Complex Singularities Workshop VII.
(accepted on 28 Jan. 2019).
The first draft: arXiv:1811.01521 [math.DG]
A draft with figures, 2018.11.23-version.
Open access to Revue...

[60] Goo Ishikawa, Tatsuya Yamashita, Leibniz complexity of Nash functions on differentiations,
Journal of the Mathematical Society of Japan, vol. 71-3 (2019), 709-726.
doi: 10.2969/jms/76877687
(accepted on 10 March 2018).
The final draft: arXiv:1509.08261 [math.AG]

[59] Goo Ishikawa, Tatsuya Yamashita, Singularities of tangent surfaces to directed curves,
Topology and its Applications, 234 (2018), 198--208
(accepted on 18 July 2017). https://doi.org/10.1016/j.topol.2017.11.018
(a special issue for the Proceedings of the 14th International Workshop on Real and Complex Singularities)
The first draft: arXiv: 1607.08702 [math.DG]

[58] Goo Ishikawa, Singularities of frontals,
in "Singularities in Generic Geometry", Advanced Studies in Pure Mathematics (ASPM), vol.78, Math. Soc. Japan, pp.55-106, (2018).
(accepted on 26 June 2017).
A draft with figures and an epigram, 2016.6.7-version.

[57] Goo Ishikawa, Stanislaw Janeczko, Residual Algebraic Restrictions of Differential Forms,
Methods and Applications of Analysis, vol. 24, No. 1 (March 2017), 045--062. (special volume dedicated to Henry Laufer’s 70th birthday)
(accepted on 13 October 2016).

[56] Goo Ishikawa, Tatsuya Yamashita, Singularities of tangent surfaces to generic space curves,
Journal of Geometry, vol.108 (2017), 301--318.
doi:10.1007/s00022-016-0341-3,
(accepted on July 1, 2016, Published online: 09 July 2016).
The first draft: arXiv:1602.02458 [math.DG]

[55]: Goo Ishikawa, Classification problems on singularities of mappings and their applications,
Sugaku Exposition, Volume 28--2 (2015), 189--214.

[54]: Goo Ishikawa, Y. Machida, Monge-Amp\`ere systems with Lagrangian pair,
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 11 (2015), 081, 32 pages.
paper
The first and final drafts: arXiv:1503.01529 [math.DG]

[53]: G. Ishikawa, Y. Machida, M. Takahashi, Geometry of D_4 conformal triality and singularities of tangent surfaces,
in Proc. of Singularities in Geometry andAppl. III, Edinburgh, Scotland, 2013,
Journal of Singularities, vol. 12 (2015), 27--52. DOI: 10.5427/jsing.2015.12c
paper
Hokkaido University Preprint Series in Mathematics #1051,

[52]: G. Ishikawa, Y. Machida, M. Takahashi, Singularities of tangent surfaces in Cartan's split G2-geometry,
Asian Journal of Mathematics, vol.20--2, (2016), 353--382.
DOI: http://dx.doi.org/10.4310/AJM.2016.v20.n2.a6
Hokkaido University Preprint Series in Mathematics #1020,

[51]: G. Ishikawa, Y. Machida, M. Takahashi, D_n-geometry and singularities of tangent surfaces,
RIMS K\={o}ky\={u}roku Bessatsu, B55 (2016), 67--87.
Hokkaido University Preprint Series in Mathematics #1058,

[50]: G. Ishikawa, Y. Kitagawa, W. Yukuno, Duality on geodesics of Cartan distributions and sub-Riemannian pseudo-product structures,
Demonstratio Mathematica. vol. 48-2 (2015, May) 193--216．
The first draft: arXiv math.DG 1403.5863

[49]: G. Ishikawa, Y. Kitagawa, W. Yukuno, Duality of singular paths for (2,3,5)-distributions,
Journal of Dynamical and Control Systems, vol. 21 (2015, February), 155--171.
DOI: 10.1007/s10883-014-9216-9
The first draft: arXiv math.DG 1308.2501

[48]: Goo Ishikawa, Openings of differentiable map-germs and unfoldings,
Topics on Real and Complex Singularities, Proceedings of the 4th Japanese-Australian Workshop (JARCS4), Kobe 2011, World Scientific (2014), 87--113.
latest manuscript

[47]: Goo Ishikawa, Tangent varieties and openings of map-germs,
RIMS K\={o}ky\={u}roku Bessatsu, B38 (2013), 119--137.
latest manuscript

[46]: Goo Ishikawa, Singularities of tangent varieties to curves and surfaces,
Journal of Singularities, 6 (2012), 54--83.
paper

[45]: G. Ishikawa, S. Janeczko, Symplectic invariants of parametric singularities,
in Proceedings of the Conference on Geometry in honour of Shing-Tung Yau's 60th Birthday, April 6--8, 2009, Warsaw, Poland,
Advances in Geometric Analysis, Advanced Lectures in Mathematics series 21, ed. by Stanislaw Janeczko, Jun Li, Duong H. Phong, International Press (2012, 31 July), pp. 259--280.
preprint: final version
preprint: first version

[44]: Goo Ishikawa, Classification problems on singularities of mappings and their applications,
Sugaku, Volume 64--1 (2012), 75-96. (In Japanese).

[43]: Goo Ishikawa, Generic bifurcations of framed curves in a space form and their envelopes,
Topology and its Applications, vol.159 (2012), 492--500.

[42]: G. Ishikawa, Y. Machida, M. Takahashi, Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality,
Journal of Singularities, vol.3 (2011), 126--143.
pdf

[41]: G. Ishikawa, S. Janeczko, Symplectic classification of parametric complex plane curves,
Annales Polonici Mathematici, vol. 99--3 (2010) 263--284.

[40]: Goo Ishikawa, Singularities of flat extensions from generic surfaces with boundaries,
Differential Geometry and its Applications, vol. 28--3 (2010) 341--354.

[39]: G. Ishikawa, S. Janeczko, Bifurcations in symplectic space,
Banach Center Publ., vol. 82 (2008), 111-124.

[38]: A.A. Davydov, G. Ishikawa, S. Izumiya, W.-Z. Sun, Generic singularities of implicit systems of first order differential equations on the plane,
Japanese Journal of Mathematics, vol. 3--1(2008) 93--119.

[37]: Goo Ishikawa, Global classification of curves on the symplectic plane,
in Proceedings of the IX Workshop on Real and Complex Singularities, Sao Carlos, 2006, Contemporary Mathematics 459, Amer. Math. Soc., (2008), pp. 51--72.
The arXiv version: arXiv:math/0702602 [math.DG]
paper

[36]: J. Adachi, G. Ishikawa, Classification of phase singularities for complex scalar waves and their bifurcations,
Nonlinearity 20 (2007) 1907--1925.

[35]: Goo Ishikawa, Zariski's moduli problem for plane branches and the classification of Legendre curve singularities. in Real and Complex Singularities,
Proceedings of the Australian-Japanese Workshop University of Sydney, Australia 5 - 8 September 2005. World Scientific (2007) pp. 56--84.

[34]: G. Ishikawa, Y. Machida, Singularities of improper affine spheres and surfaces of constant Gaussian curvature.
International Journal of Mathematics, Vol. 17--3 (2006), 269--293.

[33]: Goo Ishikawa, Infinitesimal deformations and stability of singular Legendre submanifolds. Asian Journal of Mathematics. Vol. 9 No. 1 (March 2005), 133--166.

[32]: G. Ishikawa, S. Janeczko, Symplectic singularities of isotropic mappings.
Banach Center Publications vol. 65 Geometric Singularity Theory, eds.: Heisuke Hironaka, Stanislaw Janeczko, Stanislaw Lojasiewicz. (2004), pp. 85-106.

[31]: Goo Ishikawa, Classifying singular Legendre curves by contactomorphisms.
Journal of Geometry and Physics. Vol.52--2 , (2004) 113-126.

[30]: Goo Ishikawa, Perturbations of Caustics and Fronts,
in "Geometry and Topology of Caustics --- Caustics '02", Banach Center Publications, Vol. 62, (2004), 101--116.

[29]: G. Ishikawa, S. Janeczko, Symplectic bifurcations of plane curves and isotropic liftings,
Quarterly Journal of Mathematics, Oxford, 54 (2003), 73--102.

[28]: G. Ishikawa, M. Kimura, R. Miyaoka, Submanifolds with degenerate Gauss mappings in spheres,
in ``Lie Groups, Geometric Structures and Differential Equations --- One Hundred Years after Sophus Lie ---'', Advanced Study in Pure Mathematics, 37 (2002), pp. 115--149.

[27]: I. Bogaevskii, G. Ishikawa, Lagrange mappings of the first open Whitney umbrella.
Pacific Journal of Math., 203--1 (2002), 115--138.

[26]: G. Ishikawa, T. Morimoto, Solution surfaces of the Monge-Amp\`{e}re equation.
Differential Geometry and its Applications, 14 (2001), 113--124.

[25]: Goo Ishikawa, Topological classification of the tangent developables of space curves.
Journal of London Math. Soc., 62--2 (2000), 583--598.
pdf

[24]: Goo Ishikawa, Developable submanifolds and homogeneous spaces in a real projective space,
Lobachevsky Journal of Mathematics, 3 (1999), 113--125.
pdf

[23]: Goo Ishikawa, Determinacy, Transversality and Lagrange Stability,
Banach Center Publications, Vol 50 (1999), 123--135.

[22]: Goo Ishikawa, Singularities of developable surfaces,
in Proceedings of the European Singularities Conference, August 1996, Liverpool, dedicated to C.T.C. Wall on the Occasion of his 60th Birthday, London Math. Soc. Lecture Notes Series, vol. 263, pp. 403--418, (1999).

[21]: Goo Ishikawa, A relative transversality theorem and its applications,
in Real analytic and algebraic singularities, Pitman Research Notes in Math., Vol 381 (1998), Longman Scientific and Technical., pp. 84--93.

[20]: Goo Ishikawa, Topology of plane trigonometric curves and the strangeness of plane curves derived from real psudo-line arrangements, Matem\' atica Contempor\^ anea, Vol 12 (1997), 103--129.
pdf

[19]: H. Brodersen, G. Ishikawa, L.C. Wilson, A criterion for finite topological determinacy of smooth map-germs,
Proc. London Math. Soc., Vol. 74-3 (1997), 662--700.

[18]: Goo Ishikawa, Symplectic and Lagrange stabilities of open Whitney umbrellas,
Invent. math., Vol. 126-2 (1996), 215--234.

[17]: Goo Ishikawa, Transversalities for Lagrange singularities of isotropic mappings of corank one,
in Singularities and Differential Equations, Banach Center Publications, Vol. 33 (1996), 93--104.

[16]: Goo Ishikawa, Developable of a curve and determinacy relative to osculation-type,
Quart. J. Math. Oxford, Vol.46 (1995), 437--451.

[15]: G. Ishikawa, T. Nishimura, Smooth retracts of Euclidean space,
Kodai Math. J., Vol. 18 (1995, September), pp.260--265.

[14]: Goo Ishikawa, Parametrized Legendre and Lagrange varieties,
Kodai Math. J., Vol. 17--3 (1994, October), pp.442--451.
pdf

[13]: A. Hayakawa, G. Ishikawa, S. Izumiya, K. Yamaguchi, Classification of generic integral diagrams and first order ordinary differential equations,
International J. Math., Vol. 5--4 (1994), pp.447--489.

[12]: G. Ishikawa, S. Izumiya, K. Watanabe, Vector fields near a generic submanifold, Geometriae Dedicata, Vol. 48--2 (1993, November), pp.127--137.

[11]: Goo Ishikawa, Determinacy of the envelope of the osculating hyperplanes to a curve,
Bull. London Math. Soc., 25(1993), pp.603--610.

[10]: G. Ishikawa, T. Ohmoto, Local invariants of singular surfaces in an almost complex four-manifold,
Ann. Global Anal. Geom., Vol.11 (1993), pp.125--133.

[9]: Goo Ishikawa, Maslov class of an isotropic map-germ arising from one dimensional symplectic reduction,
Adv. Stud. Pure Math., vol. 22 \lq\lq Recent Developments in Differential Geometry", (1993, September), pp.53--68.

[8]: Goo Ishikawa, Parametrization of a singular Lagrangian variety,
Trans. Amer. Math. Soc., Vol.331--2 (1992, August), pp.787--798.

[7]: Goo Ishikawa, Topologically extremal real algebraic surfaces in ${\bf P}^2\times {\bf P}^1$ and ${\bf P}^1\times {\bf P}^1\times {\bf P}^1$,
Hokkaido Math. J., Vol.21--1 (1992, February), pp.51--78.

[6]: Goo Ishikawa, The local model of an isotropic map-germ arising from one-dimensional symplectic reduction, Math. Proc. Cambridge Philo. Soc., Vol.111--1 (1992 February), pp.103--112.

[5]: T. Fukuda, G. Ishikawa. On the number of cusps of stable perturbations of a plane-to-plane singularity, Tokyo J. Math., Vol.10-2 (1987, December), pp.375-384.

[4]: Goo Ishikawa, The number of singular points in a pencil of real plane algebraic curves, Japanese J. Math., Vol.11, No.2 (1985, December), pp.387-401.

[3]: G. Ishikawa, S. Koike, M. Shiota, Critical value sets of generic mappings,
Pacific J. Math., Vol.114-1 (1984, October), pp.165-174.

[2]: Goo Ishikawa, Families of functions dominated by distributions of ${\cal C}$-classes of mappings,
Ann. Inst. Fourier, Vol.33-2 (1983, September), pp.199-217.

[1]: Goo Ishikawa, On degree of non-roughness of real projective varieties,
Proc. Japan Acad., Vol.59, Ser.A, No.6 (1983, July), pp.277-280.

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Monographs without Refereeing

[x31] Goo Ishikawa, Singularity theory viewpoints, methods and applications, in "Mathematics of Evolutionary Computation", MI Lecture Note Series Vol. 86, ISSN\UTF{2000}2188--1200, (2022), pp.51--68.

[x30] Goo Ishikawa, Tangentially bi-degenerate submanifolds, Surikaisekikenkyusho Kokyuroku, No. 2140 (2019), 102--116.

[x29] Goo Ishikawa, Catastrophe Theory in 2020 (Japanese), in Local and global study of singularity theory of differentiable maps, Surikaisekikenkyusho Kokyuroku, No. 2085 (2018), 20--35,

[x28] Goo Ishikawa, Topology and Differentiable Structures of Mapping Space Quotients, in Singularity theory of differential maps and its applications, Surikaisekikenkyusho Kokyuroku, No. 2049 (2017), 1--21,

[x27] Goo Ishikawa, Singularities of Tangent Surfaces and Generalised Frontals, Surikaisekikenkyusho Kokyuroku, No. 1948 (2015), 168--182.

[x26] Goo Ishikawa, Basic topics on tropical geometry and singularities, Surikaisekikenkyusho Kokyuroku, No. 1764 (2011), 149--164.

[x25] Goo Ishikawa, Singularity geometry of Legendre surfaces with boundaries and projective duality, Surikaisekikenkyusho Kokyuroku, No. 1664 (2009), 117--125.

[x24] Goo Ishikawa, Local classification of varieties in the symplectic space, Surikaisekikenkyusho Kokyuroku, No. 1610 (2008), 38--50.

[x23] Goo Ishikawa, A differentiable structure on a mapping space quotient and its application to the moduli problem, Surikaisekikenkyusho Kokyuroku, No. 1540 (2007), 79--90.

[x22] Goo Ishikawa, Y. Machida, Extra singularities of geometric solutions to Monge-Amp\'{e}re equations of three variables, Surikaisekikenkyusho Kokyuroku, No. 1502 (2006), 41--53.

{x21] Goo Ishikawa, Stanislaw Janeczko, The complex symplectic moduli spaces of uni-modal parametric plane curve singularities, in Singularities and Symplectic Geometry -- Part VII, Singularity Theory Seminar vol. 9/10 (2005), ed. by S. Janeczko, Warsaw University of Technology (2006), pp. 86--99.

[x20] G. Ishikawa, {\it Singular Legendre curves and Goursat systems, } in Abstracts of International Conference on Differential Equations and Dynamical Systems, Suzdal 5--10 July (2004), pp. 266--268.

[x19] Goo Ishikawa, Motivic integration in non-holonomic geometry, Surikaisekikenkyusho Kokyuroku, No. 1374 (2004), 1--14.

[x18] G. Ishikawa, Tangentially degenerate fronts and their singularities: A survey, Surikaisekikenkyusho Kokyuroku, No. 1328 (2003), 126--143.

[x17] G. Ishikawa, M. Kimura, R. Miyaoka, Submanifolds with degenerate Gauss mappings in spheres, Josai Mathematical Monographs, vol.3 (2001), 125--138.

[x16] Goo Ishikawa, Recent results on developable submanifolds: examples and classifications. Lie groups, geometric structures and differential equations---one hundred years after Sophus Lie (Japanese) (Kyoto/Nara, 1999). Surikaisekikenkyusho Kokyuroku No. 1150 (2000), 134--141.

[x15] Goo Ishikawa, Several questions on singularities: theories and applications. Singularity theory and its applications (Japanese) (Kyoto, 1999). S\=urikaisekikenky\=usho K\=oky\=uroku No. 1122 (2000), 35--48.
pdf

[x14] Goo Ishikawa, Developable hypersurfaces and algebraic homogeneous spaces in a real projective space. Homogeneous structures and theory of submanifolds (Japanese) (Kyoto, 1998). S\=urikaisekikenky\=usho K\=oky\=uroku No. 1069 (1998), 92--104.

[x13] Goo Ishikawa, Singularities of sub-Riemannian exponential mappings, conjugate loci (caustics), wave fronts, cut loci and Carnot-Carath\'{e}dory small-balls (recent results by Agrachev, El-Alaoui, Gauthier, Ge and Kupka). Topology of real singularities and related topics (Japanese) (Kyoto, 1997). S\=urikaisekikenky\=usho K\=oky\=uroku No. 1006 (1997), 121--137.

[x12] Goo Ishikawa, Topology of plane trigonometric curves and a duality for strangeness of plane curves derived from real pseudo-line arrangements. Theory of singularities for differentiable mappings: topology and applications (Japanese) (Kyoto, 1996). S\=urikaisekikenky\=usho K\=oky\=uroku No. 952 (1996), 131--146.

[x11] Goo Ishikawa, Theory of singularities in symplectic geometry. (Japanese) Geometric aspects of real singularities (Japanese) (Kyoto, 1995). S\=urikaisekikenky\=usho K\=oky\=uroku No. 926 (1995), 59--72.

[x10] Goo Ishikawa, Maslov classes of Lagrange varieties and Legendre varieties. Microlocal geometry (Kyoto, 1992). S\=urikaisekikenky\=usho K\=oky\=uroku No. 845 (1993), 53--63.

[x9] Goo Ishikawa, Basic problems on singularities of isotropic mappings. Real singularities and real algebraic geometry (Japanese) (Kyoto, 1992). S\=urikaisekikenky\=usho K\=oky\=uroku No. 815 (1992), 78--88.

[x8] Goo Ishikawa, Developable of a curve and determinacy relative to osculatioon-type, Studies on Real Singularites (Japanese) (Kyoto, 1991). S\=urikaisekikenky\=usho K\=oky\=uroku No. 764 (1991), 131--135.

[x7] Goo Ishikawa, Maslov class of an isotropic map-germ arising from one-dimensional symplectic reduction. Differential analysis and differential topological geometry (Kyoto, 1989). S\=urikaisekikenky\=usho K\=oky\=uroku No. 725 (1990), 15--46.

[x6] G. Ishikawa, {\it Lagrangian stability of a Lagrangian map-germ in a restricted class --- open Whitney umbrellas and open swallowtails}, Proceedings of the Symposium \lq\lq Singularity Theory and its Applications", 1989, Hokkaido Univ., ed. by G. Ishikawa, S. Izumiya and T. Suwa, Hokkaido Univ. Technical Report Series in Math., {\bf 12} (1989), 267--273.

[x5] Goo Ishikawa, Topics on Hilbert's 16th problem, Real Algebraic Geometry (Japanese) (Kyoto, 1989). S\=urikaisekikenky\=usho K\=oky\=uroku No. 690 (1989), 9--36.

[x4] Goo Ishikawa, Topics on real enumerative geometry, Singularities of $C^\infty$-mappings and Contact Geometry (Japanese) (Kyoto, 1987). S\=urikaisekikenky\=usho K\=oky\=uroku No. 619 (1987), 1--11.

[x3] Goo Ishikawa, Topologically extremal real surfaces in $\PP^2\times\PP^1$ and $\PP^1\times\PP^1\times\PP^1$, Complex Singularities and Commutative Rings (Japanese) (Kyoto, 1986). S\=urikaisekikenky\=usho K\=oky\=uroku No. 595 (1986), 39--58.

[x2] Goo Ishikawa, On topology of real algebraic functions, $C^\infty$-mappings and their Singularities (Japanese) (Kyoto, 1985). S\=urikaisekikenky\=usho K\=oky\=uroku No. 550 (1985), 184--202.
pdf

[x1] Goo Ishikawa, On $C^2$ stable mappings, $C^\infty$-mappings and Singular Sets (Japanese) (Kyoto, 1980). S\=urikaisekikenky\=usho K\=oky\=uroku No. 403 (1980), 88--95.

Books in Japanese (Only in Japanese)

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