Seshadri constants on surfaces with Picard number 1

TL;DR

This paper establishes lower bounds for Seshadri constants on smooth projective surfaces with Picard number 1 at multiple general points, contributing to understanding their geometric properties.

Contribution

It provides new lower bounds for Seshadri constants on surfaces with Picard number 1 at multiple points, a previously less explored area.

Findings

Lower bounds for Seshadri constants at multiple points

Results specific to surfaces with Picard number 1

Enhanced understanding of positivity properties

Abstract

Let $X$ be a smooth projective surface with Picard number 1. Let $L$ be the ample generator of the N\'eron-Severi group of $X$. Given an integer $r\ge 2$, we prove lower bounds for the Seshadri constant of $L$ at $r$ general points in $X$.