Birational self-maps of threefolds of (un)-bounded genus or gonality
Algebraic Geometry
2021-02-03 v2
Abstract
We study the complexity of birational self-maps of a projective threefold by looking at the birational type of surfaces contracted. These surfaces are birational to the product of the projective line with a smooth projective curve. We prove that the genus of the curves occuring is unbounded if and only if is birational to a conic bundle or a fibration into cubic surfaces. Similarly, we prove that the gonality of the curves is unbounded if and only if is birational to a conic bundle.
Cite
@article{arxiv.1905.00940,
title = {Birational self-maps of threefolds of (un)-bounded genus or gonality},
author = {Jérémy Blanc and Ivan Cheltsov and Alexander Duncan and Yuri Prokhorov},
journal= {arXiv preprint arXiv:1905.00940},
year = {2021}
}
Comments
23 pages, some appendix added