An effective and sharp lower bound on Seshadri constants on surfaces with Picard number 1

TL;DR

This paper establishes a precise lower bound for Seshadri constants at any point on algebraic surfaces with Picard number one, advancing understanding of local positivity in algebraic geometry.

Contribution

It provides a new, sharp lower bound for Seshadri constants specifically on surfaces with Picard number one, filling a gap in the existing literature.

Findings

Derived a sharp lower bound applicable to all points on such surfaces

Enhanced the understanding of local positivity measures in algebraic geometry

Potential applications to the study of ample line bundles and surface classification

Abstract

We study lower bounds on Seshadri constants at arbitrary points on surfaces with Picard number 1.