Finiteness results for hyperbolic orbifold pairs

TL;DR

This paper extends finiteness results for dominant maps to hyperbolic orbifold pairs, showing that under certain conditions, the set of orbifold maps and automorphisms is finite, generalizing Noguchi's theorem.

Contribution

It generalizes Noguchi's finiteness theorem to orbifold pairs, establishing new finiteness results in the orbifold setting.

Findings

Finiteness of the set of orbifold pointed maps.

Finiteness of the orbifold automorphism group.

Extension of Noguchi's theorem to orbifold pairs.

Abstract

Noguchi proved that the set of dominant maps from a fixed variety to a fixed hyperbolic variety is finite. We extend this result to the setting of orbifold pairs, as introduced by Campana, under suitable assumptions. Certain compactness properties also allow us to prove that the set of orbifold pointed maps and the orbifold automorphism group are finite.