Vol. 13, No. 9, 2019

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Brody hyperbolicity of base spaces of certain families of varieties

Mihnea Popa, Behrouz Taji and Lei Wu

Vol. 13 (2019), No. 9, 2205–2242
Abstract

We prove that quasi-projective base spaces of smooth families of minimal varieties of general type with maximal variation do not admit Zariski dense entire curves. We deduce the fact that moduli stacks of polarized varieties of this sort are Brody hyperbolic, answering a special case of a question of Viehweg and Zuo. For two-dimensional bases, we show analogous results in the more general case of families of varieties admitting a good minimal model.

Keywords
Brody hyperbolicity, minimal models, moduli of polarized varieties, varieties of general type, Green–Griffiths–Lang's conjecture, Hodge modules
Mathematical Subject Classification 2010
Primary: 14C30
Secondary: 14D07, 14E30, 14J10, 14J15, 14J29
Milestones
Received: 8 March 2019
Revised: 22 June 2019
Accepted: 10 July 2019
Published: 7 December 2019
Authors
Mihnea Popa
Department of Mathematics
Northwestern University
Evanston, IL
United States
Behrouz Taji
School of Mathematics and Statistics
The University of Sidney
NSW
Australia
Lei Wu
Department of Mathematics
University of Utah
Salt Lake City, UT
United States