Monday Analysis Seminar: An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities

2015-5-29 16:30 - 2015-5-29 18:00
Faculty of Science Buliding #3 Room 413
Shin-ichi Matsumura (Tohoku University)
In this talk, I would like to give a generalization of the cohomology
vanishing theorem to line bundles admitting singular metrics with semi-positive curvature. This result can be seen as a generalization of various injectivity and vanishing theorems. To treat transcendental singularities, after regularizing a given singular metric, we study the asymptotic behavior of the harmonic forms with respect to a family of the regularized metrics. Moreover we give a method to obtain \(L^2\)-estimates of solutions of the dbar-equation, by using the Cech complex.
If time permits, I would like to explain applications to algebraic geometry.

Different place, time and day of the week.