The theorem of Maehara-Severi for maps of general type
Algebraic Geometry
2026-04-01 v2 Complex Variables
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.
Keywords
Cite
@article{arxiv.2602.02314,
title = {The theorem of Maehara-Severi for maps of general type},
author = {Finn Bartsch and Ariyan Javanpeykar and Erwan Rousseau},
journal= {arXiv preprint arXiv:2602.02314},
year = {2026}
}
Comments
23 pages. v2 addresses some inaccuracies in v1; main results unchanged. Comments still welcome