Exceptional loci in algebraic surfaces

TL;DR

This paper investigates the algebraic exceptional set in algebraic surfaces of log general type with multiple boundary components, establishing conditions under which this set is finite or empty, advancing understanding of surface classification.

Contribution

It provides new results on the finiteness and emptiness of the exceptional set for certain algebraic surfaces with complex boundary divisors.

Findings

Exceptional set is finite or empty in most cases

Results apply to surfaces with at least three boundary components

Advances classification of algebraic surfaces of log general type

Abstract

We study the algebraic exceptional set for surfaces (S,B) of log general type, when B has at least three irreducible components; we prove that in most cases it is finite or empty.