Positivity of the Poincaré bundle on the moduli space of vector bundles and its applications

2021/06/09 by Kyoung-Seog Lee, Lee, Kyoung-Seog, Han‐Bom Moon +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2106.04857

openalex publication_date 2021/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the normalized Poincaré 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.

Related

• Derived category and ACM bundles of moduli space of vector bundles on a curve
• Projective Poincaré and Picard bundles for moduli spaces of vector bundles over nodal curves
• Poincaré bundle for the fixed determinant moduli space on a nodal curve
• Rationality of moduli of vector bundles on curves
• On Poincare bundles of vector bundles on curves