Brody hyperbolicity of base spaces of certain families of varieties

Popa, Mihnea; Taji, Behrouz; Wu, Lei

doi:10.2140/ant.2019.13.2205

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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

DOI: 10.2140/ant.2019.13.2205

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

Vol. 13, No. 9, 2019