Motivic classes of degeneracy loci and pointed Brill‐Noether varieties.

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$\chi _y$‐genus of classical and one‐pointed Brill–Noether varieties, and therefore their topological Euler characteristic, holomorphic Euler characteristic, and signature. [ABSTRACT FROM AUTHOR]