Bounds on Seshadri constants on surfaces with Picard number 1

TL;DR

This paper improves lower bounds for Seshadri constants on surfaces with Picard number 1 and extends these bounds to multiple points, advancing understanding of local positivity in algebraic geometry.

Contribution

It provides sharper lower bounds for Seshadri constants on surfaces with Picard number 1 and introduces a multi-point lower bound, enhancing previous results.

Findings

Improved lower bounds for Seshadri constants on surfaces with Picard number 1.

Established a multi-point lower bound for Seshadri constants.

Advances understanding of local positivity in algebraic geometry.

Abstract

In this note we improve a result of Steffens on the lower bound for Seshadri constants in very general points of a surface with one-dimensional N\'eron-Severi space. We also show a multi-point counterpart of such a lower bound.