Autoequivalences of Derived Categories of Moduli Spaces of Vector Bundles

Haotian Zuo

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arXiv · 2605.28846

Autoequivalences of Derived Categories of Moduli Spaces of Vector Bundles

Haotian Zuo

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Abstract

Let $C$ be a smooth projective curve over an algebraically closed field of characteristic zero. For the moduli space $N(r,L)$ of stable vector bundles on $C$ of rank $r$ with fixed determinant $L$, we study the group of exact autoequivalences of its bounded derived category. Combining the Bondal--Orlov reconstruction theorem with the descriptions of $\operatorname{Aut}(N(r,L))$ due to Kouvidakis--Pantev and Newstead, we obtain an explicit description of $\operatorname{Aut}\mathrm{D^b}(N(r,L))$. We also construct extension correspondences between moduli spaces of vector bundles of different ranks and use them to define natural Fourier--Mukai type exact functors between their bounded derived categories.

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Haotian Zuo. 2026-05-15. Autoequivalences of Derived Categories of Moduli Spaces of Vector Bundles. https://arxiv.org/abs/2605.28846

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