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Bibliographic Details
Main Authors:	Gautam, Ajay, Lin, Feiyang, Sinha, Shubham
Format:	Preprint
Published:	2025
Subjects:	Algebraic Geometry 14H60, 14M15, 14D20 14F08
Online Access:	https://arxiv.org/abs/2511.03519
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Table of Contents:

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.