On semipositivity theorems

Fujino, Osamu; Fujisawa, Taro

doi:10.4310/mrl.2019.v26.n5.a6

Cited by 7 publications

(5 citation statements)

References 13 publications

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“…[Zuo00] and [Bru,Theorem 0.6]. See also [FF17] for a different proof. From this, one can easily deduce Corollary 1.5 in the special case where the eigenvalues of the residues are rational numbers, as explained for example in [PW16].…”

Section: Statement Of the Main Resultsmentioning

confidence: 98%

Semi-positivity from Higgs bundles

Brunebarbe

2017

Preprint

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We prove a generalization of the Fujita-Kawamata-Zuo semi-positivity Theorem [Fuj78, Kaw81, Zuo00] for filtered regular meromorphic Higgs bundles and tame harmonic bundles. Our approach gives a new proof in the cases already considered by these authors. We give also an application to the geometry of smooth quasi-projective complex varieties admitting a semisimple complex local system with infinite monodromy.

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Section: Statement Of the Main Resultsmentioning

confidence: 98%

Semi-positivity from Higgs bundles

Brunebarbe

2017

Preprint

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“…We note that similar statements appear in various contexts in algebraic geometry; cf. [7,13,16,18,20,22,23,29,30,41,42,49] among many others. The fundamental results of Cattani et al [9] are an indispensable tool in the arguments of most of the articles quoted above.…”

Section: [U]mentioning

confidence: 99%

Algebraic Fiber Spaces and Curvature of Higher Direct Images

Берндтссон¹,

Păun²,

Wang³

2020

J. Inst. Math. Jussieu

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Let $p:X\rightarrow Y$ be an algebraic fiber space, and let $L$ be a line bundle on $X$ . In this article, we obtain a curvature formula for the higher direct images of $\unicode[STIX]{x1D6FA}_{X/Y}^{i}\otimes L$ restricted to a suitable Zariski open subset of $X$ . Our results are particularly meaningful if $L$ is semi-negatively curved on $X$ and strictly negative or trivial on smooth fibers of $p$ . Several applications are obtained, including a new proof of a result by Viehweg–Zuo in the context of a canonically polarized family of maximal variation and its version for Calabi–Yau families. The main feature of our approach is that the general curvature formulas we obtain allow us to bypass the use of ramified covers – and the complications that are induced by them.

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“…. Then G is locally free and G * is a nef locally free sheaf on C ′ (see [FF1,Corollary 5.23], [FFS], [FF2], [Fujisa], and so on). Since R…”

Section: Proof Of Theoremsmentioning

confidence: 99%