## Algebra & Number Theory

### Effective Matsusaka's theorem for surfaces in characteristic $p$

#### 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.

#### Article information

Source
Algebra Number Theory, Volume 9, Number 6 (2015), 1453-1475.

Dates
Revised: 16 April 2015
Accepted: 17 May 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.ant/1510842377

Digital Object Identifier
doi:10.2140/ant.2015.9.1453

Mathematical Reviews number (MathSciNet)
MR3397408

Zentralblatt MATH identifier
06488168

#### Citation

Di Cerbo, Gabriele; Fanelli, Andrea. Effective Matsusaka's theorem for surfaces in characteristic $p$. Algebra Number Theory 9 (2015), no. 6, 1453--1475. doi:10.2140/ant.2015.9.1453. https://projecteuclid.org/euclid.ant/1510842377

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