The theorem of Maehara-Severi for maps of general type

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.

23 pages. v2 addresses some inaccuracies in v1; main results unchanged. Comments still welcome