表現論セミナー Amoebas and Horn hypergeometric functions

開催日時
2014年   9月 8日 15時 00分 ~ 2014年   9月 8日 16時 30分
場所
理学部3-307
講演者
Susumu Tanabé氏 (Université Galatasaray)
 
Since 10 years, the utility of the Horn hypergeometric functions in Algebraic Geometry has been recognized in a small circle of specialists. The main reason for this interest lies in the fact that every period integral of an affine non-degenerate complete intersection variety can be described as a Horn hypergeometric function (HGF). Therefore the monodromy of the middle dimensional homology can be calculated as the monodromy of an Horn HGF’s.
There is a slight difference between the Gel’fand-Kapranov-Zelevinski HGF’s and the Horn HGF’s. The latter may contain so called “persistent polynomial solutions” that cannot be mapped to GKZ HGF’s via a natural isomorphism between two spaces of HGF’s.
In this talk, I will review basic facts on the Horn HGF’s. As a main tool to study the topology of the discriminant loci together with the analytic aspects of the story, amoebas – image by the log map of the discriminant- will be highlighted.
As an application of this theory the following theorem can be established. For a bivariate Horn HGF system, its monodromy invariant space is always one dimensional if and only if its Ore-Sato polygon is either a zonotope or a Minkowski sum of a triangle and some segments.
This is a collaboration with Timur Sadykov.


関連項目

研究集会・セミナー・集中講義の一覧へ