On the cohomology of tautological bundles over Quot schemes of curves
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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Algebraic structures and combinatorial models
Alkaloids: synthesis and pharmacology
Publication details
- Journal / source
- Algebra & Number Theory
- Volume
- 20
- Issue
- 5
- Pages
- 943–969
- Publication date
- 6 May 2026
- Language
- EN