@article{f5146236f98246dca1c51748c40b5c51,
title = "Birational self-maps of threefolds of (un)-bounded genus or gonality",
abstract = "We study the complexity of birational self-maps of a projective threefold X 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 X 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 X is birational to a conic bundle.",
author = "J{\'e}r{\'e}my Blanc and Ivan Cheltsov and Alexander Duncan and Yuri Prokhorov",
note = "Funding Information: Manuscript received May 2, 2019; revised February 2, 2021. Research supported through the programme “Research in Pairs” by the Mathematisches Forschungsinstitut Oberwolfach in 2018; research of the first author supported by the Swiss National Science Foundation Grant “Birational transformations of threefolds” 200020 178807; research of the second and fourth authors supported in part by the Royal Society grant No. IES\R1\180205, and the Russian Academic Excellence Project 5-100; research of the third author supported in part by National Security Agency grant H98230-16-1-0309. American Journal of Mathematics 144 (2022), 575–597. {\textcopyright} 2022 by Johns Hopkins University Press. Publisher Copyright: {\textcopyright} 2022 by Johns Hopkins University Press.",
year = "2022",
month = apr,
day = "30",
doi = "10.1353/ajm.2022.0011",
language = "English",
volume = "144",
pages = "575--597",
journal = "American Journal of Mathematics",
issn = "0002-9327",
publisher = "Johns Hopkins University Press",
number = "2",
}