Euler characteristics of tautological bundles over Quot schemes of curves

2022/07/04 by Dragos Oprea, Shubham Sinha, Oprea, Dragos +1 · 3 citations
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2207.01675

openalex publication_date 2022/07/04 · openalex created_date 2022/07/08 · openalex updated_date 2026/07/28

Abstract

We compute the Euler characteristics of tautological vector bundles and their exterior powers over the Quot schemes of curves. We give closed-form expressions over punctual Quot schemes in all genera. For higher rank quotients of a trivial vector bundle, we obtain answers in genus zero. We also study the Euler characteristics of the symmetric powers of the tautological bundles, for rank zero quotients.

Cited by

• Intersection Theory of Hyperquot Schemes on curves
• A Borel--Weil--Bott theorem for Quot schemes on ℙ¹
• Resolving the Singularities of Splitting Loci

Related

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