Extension Groups of Tautological Bundles on Punctual Quot Schemes of Curves

2023/05/26 by Andreas Krug, Krug, Andreas · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2305.17124

Abstract

We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of the original vector bundle on the curve. We also give a vanishing result for the push-forward along the Quot--Chow morphism of tensor and wedge products of duals of tautological bundles.

Cited by

• Intersection Theory of Hyperquot Schemes on curves
• A Borel--Weil--Bott theorem for Quot schemes on ℙ¹

Related

• Extension groups of tautological bundles on punctual Quot schemes of curves
• On the cohomology of tautological bundles over Quot schemes of curves
• Euler characteristics of tautological bundles over Quot schemes of curves
• Extension groups of tautological sheaves on Hilbert schemes
• Derived categories of Quot schemes on smooth curves and tautological bundles