Chow classes of orbit closures of skew-symmetric matrix pencils

Abstract

Let $V$ be a six-dimensional complex vector space and let $G=\operatorname{Gr}(2,Λ^2V^\vee)$ parametrize pencils of skew-symmetric $6\times6$ matrices. The group $\operatorname{PGL}(V)$ has $11$ orbits on $G$, classified by the Jordan-Kronecker canonical form. We compute the Chow class of every orbit closure in the Schubert basis of $\operatorname{CH}^*(G)$.