Springer correspondence, hyperelliptic curves, and cohomology of Fano varieties
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.05986
 Bibcode:
 2015arXiv151005986C
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 Mathematical Research Letters, Vol. 27, No. 5 (2020), pp. 12811323