Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic

Kawakami, Tatsuro

doi:10.48550/arxiv.2108.03768

Cited by 2 publications

(1 citation statement)

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“…Log liftability, liftability of log resolutions of surfaces to the ring of Witt vectors, is an active topic of research in recent years ( [CTW17], [Lac20], [ABL20], [KN20b], [Kaw21], [Nag21]). In the forthcoming paper [KTT+22a], we will show that a klt del Pezzo surface is log liftable if and only if it is quasi-F -split.…”

Section: Fano Varietiesmentioning

confidence: 99%

Fedder type criteria for quasi-$F$-splitting

Kawakami¹,

Takamatsu²,

Yoshikawa³

2022

Preprint

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Yobuko recently introduced the notion of quasi-F -splitting and F -split heights, which generalize and quantify the notion of Frobenius-splitting, and proved that F -split heights coincide with Artin-Mazur heights for Calabi-Yau varieties. In this paper, we prove Fedder type criteria of quasi-F -splittings of complete intersections, and in particular obtain an easy formula to compute Artin-Mazur heights of Calabi-Yau hypersurfaces. Moreover, as applications, we give explicit examples of quartic K3 surfaces over F 3 realizing all the possible Artin-Mazur heights, we provide explicit computations of F -split heights for all the rational double points and bielliptic surfaces, and introduce interesting phenomena concerned with inversion of adjunction, fiber products, Fano varieties, and general fibers of fibrations.

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Section: Fano Varietiesmentioning

confidence: 99%

Fedder type criteria for quasi-$F$-splitting

Kawakami¹,

Takamatsu²,

Yoshikawa³

2022

Preprint

Self Cite

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Non-log liftable log del Pezzo surfaces of rank one in characteristic five

Nagaoka

2021

Preprint

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Building upon the classification by Lacini [arXiv:2005.14544], we determine the isomorphism classes of log del Pezzo surfaces of rank one over an algebraically closed field of characteristic five either which are not log liftable over the ring of Witt vectors or whose singularities are not feasible in characteristic zero. We also show that the Kawamata-Viehweg vanishing theorem for ample Z-Weil divisors holds for log del Pezzo surfaces of rank one in characteristic five if those singularities are feasible in characteristic zero.

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Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic

Cited by 2 publications

References 50 publications

Fedder type criteria for quasi-$F$-splitting

Fedder type criteria for quasi-$F$-splitting

Non-log liftable log del Pezzo surfaces of rank one in characteristic five

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