Hochschild cohomology of partial flag varieties

Pieter Belmans (Max Planck Institute)

Wednesday 9th January 16:00-17:00 Maths 311B

Abstract

The Hochschild-Kostant-Rosenberg decomposition gives a description of the Hochschild cohomology of a smooth projective variety in terms of the sheaf cohomology of exterior powers of the tangent bundle. In all but a few cases it is a non-trivial task to compute this decomposition, and understand the extra algebraic structure which exists on Hochschild cohomology. I will give a general introduction to Hochschild cohomology and this decomposition, and how this problem can be studied for partial flag varieties (i.e. varieties of the form G/P for G a semisimple algebraic group and P a parabolic subgroup), in particular for the case of maximal parabolic subgroups (i.e. Grassmannians in type A and their analogues in other types). This is joint work in progress with Maxim Smirnov.

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