Rigid divisors on surfaces

TL;DR

This paper investigates special effective divisors on algebraic surfaces, providing a numerical criterion for their rigidity and negativity, with applications to singularity theory and spherelike divisors.

Contribution

It introduces a new numerical criterion characterizing rigid divisors on surfaces, expanding understanding of their negativity and connectivity properties.

Findings

Criteria for rigidity of divisors established

Examples include exceptional loci of rational singularities

Analysis of negativity and connectivity properties

Abstract

We study effective divisors $D$ on surfaces with $H^0(\mathcal O_D)=k$ and $H^1(\mathcal O_D)=H^0(\mathcal O_D(D))=0$. We give a numerical criterion for such divisors, following a general investigation of negativity, rigidity and connectivity properties. Examples include exceptional loci of rational singularities, and spherelike divisors.