On the cohomology of tautological bundles over Quot schemes of curves

Marian, Alina; Oprea, Dragos; Sam, Steven V

doi:10.2140/ant.2026.20.943

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On the cohomology of tautological bundles over Quot schemes of curves

Alina Marian, Dragos Oprea and Steven V Sam

Vol. 20 (2026), No. 5, 943–969

DOI: 10.2140/ant.2026.20.943

Abstract

We consider tautological bundles and their exterior and symmetric powers on the Quot scheme over the projective line. We prove and conjecture several statements regarding the vanishing of their higher cohomology, and we describe their spaces of global sections via tautological constructions. To this end, we make use of the embedding of the Quot scheme as an explicit local complete intersection in the product of two Grassmannians, studied by Strømme. This allows us to construct resolutions with vanishing cohomology for the tautological bundles and their exterior and symmetric powers. We further illustrate our approach with a few additional cohomological calculations.

Keywords

Quot scheme, sheaf cohomology

Mathematical Subject Classification

Primary: 14H60, 14M99

Milestones

Received: 21 June 2023

Revised: 17 April 2025

Accepted: 22 May 2025

Published: 6 May 2026

Authors

Alina Marian
Department of Mathematics Northeastern University Boston, MA United States

Dragos Oprea
Department of Mathematics University of California San Diego La Jolla, CA United States

Steven V Sam
Department of Mathematics University of California San Diego La Jolla, CA United States

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Vol. 20, No. 5, 2026