paper

Chern class formulas for classical-type degeneracy loci

arXiv:1504.03615 · doi:10.1112/S0010437X18007224

Abstract

In previous work, we employed a geometric method of Kazarian to prove Pfaffian formulas for a certain class of degeneracy loci in types B, C, and D. Here we refine that approach to obtain formulas for more general loci, including those coming from all isotropic Grassmannians. In these cases, the formulas recover the remarkable theta- and eta-polynomials of Buch, Kresch, Tamvakis, and Wilson. The streamlined geometric approch yields simple and direct proofs, which proceed in parallel for all four classical types. In an appendix, we develop some foundational algebra and prove several Pfaffian identities. Another appendix establishes a basic formula for classes in quadric bundles.

32 pages; v2 corrects the definitions of triples and partitions in sections 2 and 4, and clarifies the relationship with the (typed) k-strict partitions of Buch-Kresch-Tamvakis; v3 includes corrections to the published version, specifically in condition (d3) of Section 4, and Lemma 1 of Section A.3; v4 replaces (c4) and (d4) with less restrictive conditions

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