Seshadri fibrations of algebraic surfaces

TL;DR

This paper refines the understanding of how local Seshadri constants on algebraic surfaces influence their global fibration structures, extending previous results to measurements at finite subsets.

Contribution

It extends prior work by showing that Seshadri constants at finite subsets also determine the fibration structure of algebraic surfaces.

Findings

Seshadri constants at finite subsets relate to surface fibrations

Refinement of previous results by Hwang, Keum, Szemberg, Tutaj-Gasinska

Global geometry can be inferred from local invariants

Abstract

We refine results of Hwang, Keum and Szemberg, Tutaj-Gasinska which relate local invariants - Seshadri constants - of ample line bundles on surfaces to the global geometry - fibration structure. We show that the same picture emerges when looking at Seshadri constants measured at any finite subset of the given surface.