Free quotients of fundamental groups of smooth quasi-projective varieties

TL;DR

This paper investigates the structure of certain curve classes on projective surfaces, focusing on when their complements' fundamental groups admit large free quotients, and establishes finiteness results under specific conditions.

Contribution

It provides new insights into the relationship between curve classes on surfaces and the free quotients of their fundamental groups, including finiteness results for large ranks.

Findings

Finiteness results for classes with large free quotients

Characterization of curves with fundamental groups admitting free quotients

Conditions under which free quotients of fundamental groups are constrained

Abstract

We consider the structure of classes of curves on a projective simply connected surface for which fundamental groups of the complements admit free quotients having rank greater than one with irreducible components belonging to a selected subset the effective cone of the surface. In particular we show a finiteness result for such classes if the ranks of free quotients of the fundamental groups with components in the subset of effective cone are sufficiently large.

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