Ben Tighe : Symmetries and vanishing theorems for symplectic varieties

Posted by Ben Bakker , part of the Algebraic Geometry Seminar.

At

April 16, 2025, 3 p.m.

In

636 SEO

Abstract

I will discuss some vanishing results for symplectic varieties which generalize the rational and Du Bois properties for singularities. These vanishing theorems arise from Hodge-theoretic symmetries on the Du Bois and intersection cohomology complex which generalize the extra symmetries you see on the Hodge diamond of a compact hyperkahler manifold. Along the way, I will discuss why these vanishing theorems are related to the existence of symplectic resolutions of singularities, new perspectives in deformation theory, and the LLV algebra.