A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$

Ajay Gautam; Feiyang Lin; Shubham Sinha

A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$

Algebraic Geometry 2025-11-06 v1

Authors: Ajay Gautam , Feiyang Lin , Shubham Sinha

Abstract

We study the cohomology groups of tautological bundles on Quot schemes over the projective line, which parametrize rank $r$ quotients of a vector bundle $V$ on $\mathbb{P}^1$ . Our main result is an analogue of the Borel--Weil--Bott theorem for Quot schemes. As a corollary, we prove recent conjectures of Marian, Oprea, and Sam on the exterior and symmetric powers of tautological bundles.

Keywords

Quot schemes tautological bundles Borel-Weil-Bott theorem projective line cohomology groups

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@article{arxiv.2511.03519,
  title  = {A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$},
  author = {Ajay Gautam and Feiyang Lin and Shubham Sinha},
  journal= {arXiv preprint arXiv:2511.03519},
  year   = {2025}
}

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33 pages

A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$

Abstract

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