The analogue of the Borel-Weil-Bott theorem reveals key properties of cohomology groups in Quot schemes, suggesting advancements in bundle theory.
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 P¹. 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.
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Gautam et al. (2025) studied this question.
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