Seshadri constants of curve configurations on surfaces

TL;DR

This paper investigates multi-point Seshadri constants at singular points of curve arrangements on surfaces, focusing on star arrangements and comparing configurational constants with traditional ones.

Contribution

It introduces new results on Seshadri constants for specific curve arrangements and explores their properties and differences from classical constants.

Findings

Proved results for star arrangements of curves.

Compared configurational and usual Seshadri constants.

Provided examples illustrating key properties.

Abstract

Let $X$ be a complex nonsingular projective surface and let $L$ be an ample line bundle on $X$. We study multi-point Seshadri constants of $L$ at singular points of certain arrangements of curves on $X$. We pose some questions about such Seshadri constants and prove some results in the case of star arrangements of curves. We also study the configurational Seshadri constants for curve arrangements on surfaces and compare them with the usual Seshadri constants. We give several examples illustrating the properties that we study.