Effective Matsusaka’s theorem for surfaces in characteristic p

Gabriele Di Cerbo; Andrea Fanelli

doi:10.2140/ant.2015.9.1453

Effective Matsusaka’s theorem for surfaces in characteristic p

Gabriele Di Cerbo, Andrea Fanelli

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We obtain an effective version of Matsusaka’s theorem for arbitrary smooth algebraic surfaces in positive characteristic, which provides an effective bound on the multiple that makes an ample line bundle D very ample. The proof for pathological surfaces is based on a Reider-type theorem. As a consequence, a Kawamata–Viehweg-type vanishing theorem is proved for arbitrary smooth algebraic surfaces in positive characteristic.

Original language	English (US)
Pages (from-to)	1453-1475
Number of pages	23
Journal	Algebra and Number Theory
Volume	9
Issue number	6
DOIs	https://doi.org/10.2140/ant.2015.9.1453
State	Published - Sep 22 2015

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Bend-and-break
Bogomolov’s stability
Effective Kawamata–Viehweg vanishing
Effective Matsusaka
Fujita’s conjectures
Reider’s theorem
Surfaces in positive characteristic

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10.2140/ant.2015.9.1453

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title = "Effective Matsusaka{\textquoteright}s theorem for surfaces in characteristic p",

abstract = "We obtain an effective version of Matsusaka{\textquoteright}s theorem for arbitrary smooth algebraic surfaces in positive characteristic, which provides an effective bound on the multiple that makes an ample line bundle D very ample. The proof for pathological surfaces is based on a Reider-type theorem. As a consequence, a Kawamata–Viehweg-type vanishing theorem is proved for arbitrary smooth algebraic surfaces in positive characteristic.",

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author = "{Di Cerbo}, Gabriele and Andrea Fanelli",

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T1 - Effective Matsusaka’s theorem for surfaces in characteristic p

AU - Di Cerbo, Gabriele

AU - Fanelli, Andrea

PY - 2015/9/22

Y1 - 2015/9/22

N2 - We obtain an effective version of Matsusaka’s theorem for arbitrary smooth algebraic surfaces in positive characteristic, which provides an effective bound on the multiple that makes an ample line bundle D very ample. The proof for pathological surfaces is based on a Reider-type theorem. As a consequence, a Kawamata–Viehweg-type vanishing theorem is proved for arbitrary smooth algebraic surfaces in positive characteristic.

AB - We obtain an effective version of Matsusaka’s theorem for arbitrary smooth algebraic surfaces in positive characteristic, which provides an effective bound on the multiple that makes an ample line bundle D very ample. The proof for pathological surfaces is based on a Reider-type theorem. As a consequence, a Kawamata–Viehweg-type vanishing theorem is proved for arbitrary smooth algebraic surfaces in positive characteristic.

KW - Bend-and-break

KW - Bogomolov’s stability

KW - Effective Kawamata–Viehweg vanishing

KW - Effective Matsusaka

KW - Fujita’s conjectures

KW - Reider’s theorem

KW - Surfaces in positive characteristic

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JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 6

ER -

Effective Matsusaka’s theorem for surfaces in characteristic p

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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