Pure and Applied Mathematics Quarterly

Volume 10 (2014)

Number 2

Special Issue: In Memory of Andrey Todorov, Part 3 of 3

Goodness of canonical metrics on the moduli space of Riemann surfaces

Pages: 223 – 243

DOI: https://dx.doi.org/10.4310/PAMQ.2014.v10.n2.a2

Authors

Kefeng Liu (Center of Mathematical Sciences, Zhejiang University, Zhejiang, China; and Department of Mathematics, University of California at Los Angeles)

Xiaofeng Sun (Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania, U.S.A.)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

In this paper we will show the Mumford goodness of the metrics on the logarithmic tangent bundle of the moduli spaces of curves induced by the Ricci and the perturbed Ricci metrics. It follows from these estimates that the Ricci metric can be extended to the Deligne-Mumford compactification of the moduli spaces.

Keywords

canonical metrics, Mumford goodness, moduli spaces, natuality

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Published 7 October 2014