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 χ y $\chi _y$ -genus of classical and one-pointed Brill–Noether varieties, and therefore their topological Euler characteristic, holomorphic Euler characteristic, and signature.