Picard theorems for moduli spaces of polarized varieties

Deng, Yansha; Lu, Shuaiyao; Sun, Ruiran; Zuo, Kang

doi:10.48550/arxiv.1911.02973

Cited by 6 publications

(13 citation statements)

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“…The following applications refine some recent results of Deng [Den20]. However, our approach differs from his: on the one hand, while Deng uses an ad hoc Finsler metric, we rely on the Griffiths-Schmid metric, and on the other hand, while Deng relies on the big Picard theorem from [DLSZ19], we use our Theorem 1.1.…”

Section: Two Applicationsmentioning

confidence: 66%

Arakelov-Nevanlinna inequalities for variations of Hodge structures and applications

Brotbek,

Brunebarbe

2020

Preprint

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We prove a Second Main Theorem type inequality for any log-smooth projective pair (X, D) such that X \ D supports a complex polarized variation of Hodge structures. This can be viewed as a Nevanlinna theoretic analogue of the Arakelov inequalities for variations of Hodge structures due to Deligne, Peters and Jost-Zuo. As an application, we obtain in this context a criterion of hyperbolicity that we use to derive a vast generalization of a well-known hyperbolicity result of Nadel.The first ingredient of our proof is a Second Main Theorem type inequality for any log-smooth projective pair (X, D) such that X \ D supports a metric whose holomorphic sectional curvature is bounded from above by a negative constant. The second ingredient of our proof is an explicit bound on the holomorphic sectional curvature of the Griffiths-Schmid metric constructed from a variation of Hodge structures.As a byproduct of our approach, we also establish a Second Main Theorem type inequality for pairs (X, D) such that X \ D is hyperbolically embedded in X.

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Section: Two Applicationsmentioning

confidence: 66%

Arakelov-Nevanlinna inequalities for variations of Hodge structures and applications

Brotbek,

Brunebarbe

2020

Preprint

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“…(4) We recall the classical Picard theorems, the so-called little Picard theorem and big Picard theorem in complex one variable and their generalizations to higher dimensional varieties. We stetch the proof in the paper [11] for the Picard extension theorem on a base parametrizing smooth varierties with semi-ample canonical line bundles.…”

Section: • the Rigidity Of Points In Hmentioning

confidence: 99%

“…Theorem 5.2.1. ( Deng-Lu-Sun-Zuo [11] Picard extension theorem on moduli stacks) Let U be a quasiprojective manifold with a smooth projective compactification Ȳ ⊃ U. Let f : V → U is family of n-folds with semi-ample canonical sheaf ω , and assume the classfying map from U to the moduli space is quasi finite.…”

Section: Picard Extension Theorem On Moduli Stacks the Classical Pica...mentioning

confidence: 99%

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Hodge Theory and Higgs Bundle on Moduli Spaces of Smooth Varieties with Semi-Ample Canonical Line Bundles, Negativity and Hyperbolicity

Zuo¹

2022

Preprint

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“…In [DLSZ19] the second named author with Lu, Sun and Zuo proved the Picard hyperbolicity for moduli of polarized manifolds with semi-ample canonical sheaf. In [Den20b], the second named author proved Theorems A and B when the nilpotent harmonic bundle ( , , ℎ) is moreover a complex polarized variation of Hodge structures.…”

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confidence: 99%

Picard hyperbolicity of manifolds admitting nilpotent harmonic bundles

Cadorel,

Deng

2021

Preprint

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BENOÎT CADOREL AND YA DENG A. For a quasi-compact Kähler manifold endowed with a nilpotent harmonic bundle whose Higgs field is injective at one point, we prove that is pseudo-algebraically hyperbolic, pseudo-Picard hyperbolic, and is of log general type. Moreover, we prove that there is a finite unramified cover ˜ of from a quasi-projective manifold ˜ so that any projective compactification of ˜ is pseudo-algebraically hyperbolic, pseudo-Picard hyperbolic and is of general type. As a byproduct, we establish some criterion of pseudo-Picard hyperbolicity and pseudo-algebraic hyperbolicity for quasi-compact Kähler manifolds.

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Picard theorems for moduli spaces of polarized varieties

Cited by 6 publications

References 0 publications

Arakelov-Nevanlinna inequalities for variations of Hodge structures and applications

Arakelov-Nevanlinna inequalities for variations of Hodge structures and applications

Hodge Theory and Higgs Bundle on Moduli Spaces of Smooth Varieties with Semi-Ample Canonical Line Bundles, Negativity and Hyperbolicity

Picard hyperbolicity of manifolds admitting nilpotent harmonic bundles

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