Moving curves and Seshadri constants

TL;DR

This paper investigates families of curves on projective surfaces to establish lower bounds on their self-intersection numbers, leading to new insights into Seshadri constants and surface geometry.

Contribution

It provides improved inequalities for curve families on surfaces and applies these to advance understanding of Seshadri constants and surface geometry.

Findings

Established new lower bounds on self-intersection of curve families

Derived novel inequalities impacting Seshadri constants

Enhanced understanding of the geometry of algebraic surfaces

Abstract

We study families of curves covering a projective surface and give lower bounds on the self-intersection of the members of such families, improving results of Ein-Lazarsfeld and Xu. We apply the obtained inequalities to get new insights on Seshadri constants and geometry of surfaces.