Springer correspondence, hyperelliptic curves, and cohomology of Fano varieties

Tsao-Hsien Chen; Kari Vilonen; Ting Xue

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arXiv · 1510.05986

Springer correspondence, hyperelliptic curves, and cohomology of Fano varieties

Tsao-Hsien Chen·Kari Vilonen·Ting Xue

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Abstract

In \cite{CVX3}, we have established a Springer theory for the symmetric pair $(\operatorname{SL}(N),\operatorname{SO}(N))$. In this setting we obtain representations of (the Tits extension) of the braid group rather than just Weyl group representations. These representations arise from cohomology of families of certain (Hessenberg) varieties. In this paper we determine the Springer correspondence explicitly for IC sheaves supported on order 2 nilpotent orbits. In this process we encounter universal families of hyperelliptic curves. As an application we calculate the cohomolgy of Fano varieties of $k$-planes in the smooth intersection of two quadrics in an even dimensional projective space.

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BibTeX RIS

Tsao-Hsien Chen, Kari Vilonen, Ting Xue. 2021-01-13. Springer correspondence, hyperelliptic curves, and cohomology of Fano varieties. https://arxiv.org/abs/1510.05986

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