Discrete behavior of Seshadri constants on surfaces

TL;DR

This paper proves that, except for possibly one limit point, the multi-point Seshadri constants on smooth projective surfaces are discrete, providing new bounds and insights into their behavior.

Contribution

It establishes the discreteness of multi-point Seshadri constants on surfaces and offers improved bounds and new results for specific cases like P^2.

Findings

Multi-point Seshadri constants are discrete except possibly at one limit point.

Provides significantly improved explicit lower bounds for Seshadri constants on P^2.

Derives new results about ample divisors on blow ups of P^2 at general points.

Abstract

Working over C, we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constant for general points on smooth projective surfaces form a discrete set. In addition to its theoretical interest, this result is of practical value, which we demonstrate by giving significantly improved explicit lower bounds for Seshadri constants on P^2 and new results about ample divisors on blow ups of P^2 at general points.