Asian Journal of Mathematics
Volume 23 (2019)
An explicit Ricci potential for the universal moduli space of vector bundle
Pages: 369 – 382
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.
universal moduli spaces, vector bundles, Ricci potential, Kähler coordinates
2010 Mathematics Subject Classification
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