The theorem of Maehara-Severi for maps of general type

TL;DR

This paper proves a finiteness theorem for dominant rational maps with orbifold bases of general type, extending Maehara's theorem and addressing questions on Bogomolov sheaves.

Contribution

It generalizes Maehara's finiteness theorem to orbifold bases and provides new finiteness results for maps to various varieties.

Findings

Finiteness of dominant rational maps with orbifold bases of general type.

Extension of Maehara's theorem to orbifold settings.

Finiteness results for maps to curves, abelian varieties, and K3 surfaces.

Abstract

We prove a finiteness result for dominant rational maps whose orbifold base is of general type. Our finiteness result generalizes Maehara's theorem that a given variety dominates only finitely many projective varieties of general type up to birational equivalence, and also answers a question of Campana on the finiteness of Bogomolov sheaves. We give several further applications, including finiteness results for maps to curves, abelian varieties, and K3 surfaces.