Symmetric differentials and variations of Hodge structures

Brunebarbe, Yohan

doi:10.1515/crelle-2015-0109

Cited by 26 publications

(56 citation statements)

References 31 publications

(46 reference statements)

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“…0 is a weakly positive sheaf by [PW16, Theorem 4.8] (an easy consequence of the results of [Zuo00] and [Bru15] in the unipotent case), so this would imply that F −1 0 is also a pseudoeffective line bundle, a contradiction.…”

Section: Main Construction On Cmentioning

confidence: 99%

Brody hyperbolicity of base spaces of certain families of varieties

Popa

Taji²,

2019

Alg. Number Th.

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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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Section: Main Construction On Cmentioning

confidence: 99%

Brody hyperbolicity of base spaces of certain families of varieties

Popa

Taji²,

2019

Alg. Number Th.

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“…The argument is in fact simpler, as no torsion issues arise. The weak positivity of [PW] (see Theorem 4.9 and its proof, a step towards the proof of Theorem 18.1) as a quick corollary of the results of [Zuo00] and [Bru15].…”

Section: Positivity For Hodge Modulesmentioning

confidence: 99%

Viehweg’s hyperbolicity conjecture for families with maximal variation

Popa

Schnell

2016

Invent. math.

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Abstract. We use the theory of Hodge modules to construct Viehweg-Zuo sheaves on base spaces of families with maximal variation and fibers of general type; and, more generally, families whose geometric generic fiber has a good minimal model. Combining this with a result of Campana-Pȃun, we deduce Viehweg's hyperbolicity conjecture in this context, namely the fact that the base spaces of such families are of log general type. This is approached as part of a general problem of identifying what spaces can support Hodge theoretic objects with certain positivity properties.

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“…It turns out that there is a more general result, which holds at each step of the Hodge filtration; this is very useful for applications. It has its origin in previous results of Zuo [Zuo00] and Brunebarbe [Bru15], which are analogous Griffiths-type metric statements in the setting of Deligne canonical extensions over a simple normal crossings boundary. Concretely, for each p we have a natural Kodaira-Spencer type O X -module homomorphism One can show that Theorem 4.3 implies Theorem 4.1 via duality arguments.…”

Section: Weak Positivitymentioning

confidence: 73%