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

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.

References in corpus (6)

• Semiorthogonal decomposition for algebraic varieties
• Degeneration of moduli spaces and generalized theta functions
• Derived categories of curves as components of Fano manifolds
• Remarks on motives of moduli spaces of rank 2 vector bundles on curves
• Motivic decompositions of moduli spaces of vector bundles on curves
• Finite generation of the algebra of type A conformal blocks via birational geometry II: higher genus