Effective Matsusaka’s theorem for surfaces in characteristic p

Gabriele Di Cerbo, Andrea Fanelli

Research output: Contribution to journalArticlepeer-review

12 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 languageEnglish (US)
Pages (from-to)1453-1475
Number of pages23
JournalAlgebra and Number Theory
Volume9
Issue number6
DOIs
StatePublished - Sep 22 2015
Externally publishedYes

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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