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Brody hyperbolicity of
base spaces of certain families of varieties
Mihnea Popa, Behrouz Taji and Lei Wu |
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Vol. 13 (2019), No. 9, 2205–2242
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Abstract |
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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. |
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Keywords
Brody hyperbolicity, minimal models, moduli of polarized
varieties, varieties of general type,
Green–Griffiths–Lang's conjecture, Hodge modules
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Mathematical Subject Classification 2010
Primary: 14C30
Secondary: 14D07, 14E30, 14J10, 14J15, 14J29
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Milestones
Received: 8 March 2019
Revised: 22 June 2019
Accepted: 10 July 2019
Published: 7 December 2019
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Authors |
| Mihnea Popa | |
| Department of Mathematics Northwestern University Evanston, IL United States |
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| Behrouz Taji | |
| School of Mathematics and
Statistics The University of Sidney NSW Australia |
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| Lei Wu | |
| Department of Mathematics University of Utah Salt Lake City, UT United States |
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