On the cohomology of Fano varieties and the Springer correspondence

TL;DR

This paper calculates the cohomology of Fano varieties of k-planes in certain complete intersections of quadrics, utilizing Springer theory for symmetric spaces to advance understanding in algebraic geometry.

Contribution

It introduces a novel application of Springer theory to compute cohomology of specific Fano varieties, connecting algebraic geometry with representation theory.

Findings

Explicit cohomology computations for Fano varieties of k-planes.

New connections established between Fano varieties and Springer theory.

Enhanced understanding of the topology of these algebraic varieties.

Abstract

In this paper we compute the cohomology of the Fano varieties of $k$-planes in the smooth complete intersection of two quadrics in $\mathbb{P}^{2g+1}$, using Springer theory for symmetric spaces.