Bijective Cremona transformations of the plane
Algebraic Geometry
2022-03-22 v4
Abstract
We study the birational self-maps of the projective plane over finite fields that induce permutations on the set of rational points. As a main result, we prove that no odd permutation arises over a non-prime finite field of characteristic two, which completes the investigation initiated by Cantat about which permutations can be realized this way. Main ingredients in our proof include the invariance of parity under groupoid conjugations by birational maps, and a list of generators for the group of such maps.
Keywords
Cite
@article{arxiv.1910.05302,
title = {Bijective Cremona transformations of the plane},
author = {Shamil Asgarli and Kuan-Wen Lai and Masahiro Nakahara and Susanna Zimmermann},
journal= {arXiv preprint arXiv:1910.05302},
year = {2022}
}
Comments
51 pages, removed section 5.A and made improvements on exposition, to appear in Selecta Mathematica