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arXiv · 2010.05928

Motivic classes of degeneracy loci and pointed Brill-Noether varieties

Dave Anderson·Linda Chen·Nicola Tarasca
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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 $\chi_y$-genus of classical and one-pointed Brill-Noether varieties, and therefore their topological Euler characteristic, holomorphic Euler characteristic, and signature.

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Dave Anderson, Linda Chen, Nicola Tarasca. 2020-10-12. Motivic classes of degeneracy loci and pointed Brill-Noether varieties. https://arxiv.org/abs/2010.05928

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