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arXiv · 2106.04857

Positivity of the Poincar\'e bundle on the moduli space of vector bundles and its applications

Kyoung-Seog Lee·Han-Bom Moon
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Abstract

We prove that the normalized Poincar\'e bundle on the moduli space of stable rank $r$ vector bundles with a fixed determinant on a smooth projective curve $X$ induces a family of nef vector bundles on the moduli space. Two applications follow. We show that when the genus of $X$ is large, the derived category of $X$ is embedded into the derived category of the moduli space for arbitrary rank and coprime degree, which extends the results of Narasimhan, Fonarev-Kuznetsov, and Belmans-Mukhopadhyay. As the second application, we construct a family of ACM bundles on the moduli space. A key ingredient of our proof is the investigation of birational geometry of the moduli spaces of parabolic bundles.

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Kyoung-Seog Lee, Han-Bom Moon. 2021-06-09. Positivity of the Poincar\'e bundle on the moduli space of vector bundles and its applications. https://arxiv.org/abs/2106.04857

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