Effective bounds on singular surfaces in positive characteristic

TL;DR

This paper establishes effective bounds for the very ampleness of certain divisors on Kawamata log terminal surfaces in positive characteristic, utilizing Frobenius singularities theory.

Contribution

It provides explicit bounds on divisors' ampleness for surfaces in positive characteristic, advancing understanding of Frobenius singularities in algebraic geometry.

Findings

13mK_X + 45mA is very ample under given conditions

Bound applies to surfaces over fields with characteristic p>5

Results improve previous bounds on divisors in positive characteristic

Abstract

Using the theory of Frobenius singularities, we show that 13mK_X + 45mA is very ample for an ample Cartier divisor A on a Kawamata log terminal surface X with Gorenstein index m, defined over an algebraically closed field of characteristic p>5.