Motivic classes of degeneracy loci and pointed Brill-Noether varieties

Abstract

Motivic Chern and Hirzebruch classes are polynomials with K-theory and homology classes as coefficients, which specialize to Chern-Schwartz-MacPherson classes, K-theory classes, and Cappell-Shaneson L-classes. We provide formulas to compute the motivic Chern and Hirzebruch classes of Grassmannian and vexillary degeneracy loci. We apply our results to obtain the Hirzebruch χy-genus of classical and one-pointed Brill-Noether varieties, and therefore their topological Euler characteristic, holomorphic Euler characteristic, and signature. MSC2020. 14N15, 14H51 (primary), 19E99 (secondary).

A pointed Prym-Petri Theorem

“…In the case of Brill-Noether varieties of line bundles with prescribed vanishing at two points, a new determinantal formula in type A was introduced in [ACT1] to compute their classes. For this, the study of two-pointed Prym-Brill-Noether varieties could lead to the computation of a new degeneracy locus formula in type D. Also, it would be interesting to compute the motivic invariants of Prym-Brill-Noether varieties, as done for the Brill-Noether varieties in [PP,ACT1,CP,ACT2].…”