The moduli space of holomorphic chains of rank one over a compact Riemann surface

2022/10/21 by Jin Hyung To, To, Jin Hyung
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2210.12292

Abstract

A holomorphic chain on a compact Riemann surface is a tuple of vector bundles together with homomorphisms between them. We show that the moduli space of holomorphic chains of rank one is identified with a fiber product of projective space bundles. We compute the Euler characteristic of the moduli space. The stability of chains involves real vector parameters. We also show that the variation of parameters corresponds to the characters of Gm.

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