Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (3 of 3)
Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University
Augmented Weil–Petersson metrics on moduli spaces of polarized Ricci-flat Kähler manifolds and orbifolds
Pages: 705 – 728
We show that the base complex manifold of an effectively parametrized family of compact polarized Ricci-flat Kähler orbifolds, and in particular manifolds, admits a smooth augmented Weil–Petersson metric whose holomorphic sectional curvature is bounded above by a negative constant. As a consequence, we conclude that such base manifold is Kobayashi hyperbolic.
augmented Weil–Petersson metric, moduli space, Ricci-flat Kähler manifolds, Kähler orbifolds
2010 Mathematics Subject Classification
32G13, 32Q25, 32Q45
Wing-Keung To was partially supported by the research grant R-146-000-142-112 from the National University of Singapore and the Ministry of Education.
Sai-Kee Yeung was partially supported by a grant from the National Science Foundation.
Received 13 September 2016
Accepted 2 June 2017
Published 20 September 2018