Coordinates for the Universal Moduli Space of Holomorphic Vector Bundles

2016/02/29 by Jørgen Ellegaard Andersen, Andersen, Jørgen Ellegaard, Niccolo Skovgård Poulsen +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1603.00294

openalex publication_date 2016/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we provide two ways of constructing complex coordinates on the moduli space of pairs of a Riemann surface and a stable holomorphic vector bundle centred around any such pair. We compute the transformation between the coordinates to second order at the center of the coordinates. We conclude that they agree to second order, but not to third order at the center.

Citations

• Asymptotics of Toeplitz operators and applications in TQFT
• Invariants of 3-manifolds via link polynomials and quantum groups

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• An explicit Ricci potential for the Universal Moduli Space of Vector Bundles
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