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arXiv · 2411.08695

Derived categories of Quot schemes on smooth curves and tautological bundles

Alina Marian·Andrei Neguţ
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Abstract

We define a categorical action of the shifted quantum loop group of $\mathfrak{sl}_2$ on the derived categories of Quot schemes of finite length quotient sheaves on a smooth projective curve. As an application, we obtain a semi-orthogonal decomposition of the derived categories of Quot schemes, of representation theoretic origin. We use this decomposition to calculate the cohomology of interesting tautological vector bundles over the Quot scheme.

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Alina Marian, Andrei Neguţ. 2024-11-13. Derived categories of Quot schemes on smooth curves and tautological bundles. https://arxiv.org/abs/2411.08695

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