An explicit Ricci potential for the universal moduli space of vector bundle

In this paper we modify our coordinate construction in “Coordinates for the Universal Moduli Space of Holomorphic Vector Bundles” [Travaux Math., XXV (2017), pp. 9–39] on the universal moduli space of pair consisting of a Riemann surfaces and a stable holomorphic bundles on the Riemann surface, so as to produce a new set of coordinates, which are in fact Kähler coordinates on this universal moduli space. Using our Kähler coordinates, we are able to give a functional determinant formula for the Ricci potential of the universal moduli space. As a corollary we compute the first Chern-class of the universal moduli space.

Keywords

universal moduli spaces, vector bundles, Ricci potential, Kähler coordinates

2010 Mathematics Subject Classification

14H60

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Research supported in part by the center of excellence grant “Center for Quantum Geometry of Moduli Spaces (QGM)” DNRF95 from the Danish National Research Foundation.

Received 27 October 2017

Accepted 8 November 2017

Published 9 July 2019