Universal degeneracy classes for vector bundles on ℙ¹ bundles

2019/06/25 by Hannah Larson, Larson, Hannah K.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1906.10290

openalex publication_date 2019/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a vector bundle on a ℙ¹ bundle, the base is stratified by degeneracy loci measuring the spitting type of the vector bundle restricted to each fiber. The classes of these degeneracy loci in the Chow ring or cohomology ring of the base are natural invariants characterizing the degenerations of the vector bundle. When these degeneracy loci occur in the expected codimension, we find their classes. This yields universal formulas for degeneracy classes in terms of naturally arising vector bundles on the base. Our results hold over arbitrary fields of any characteristic.

Citations

• Flags, Schubert polynomials, degeneracy loci, and determinantal formulas
• A refined Brill–Noether theory over Hurwitz spaces

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