On the set of fixed points of a polynomial automorphism
Algebraic Geometry
2014-09-30 v1
Abstract
Let K be an algebraically closed field of characteristic zero. We say that a polynomial automorphism f : K^n -> K^n is special if the Jacobian of f is equal to 1. We show that every (n - 1)-dimensional component H of the set Fix(f) of fixed points of a non-trivial special polynomial automorphism f : K^n -> K^n is uniruled. Moreover, we show that if f is non-special and H is an (n-1)-dimensional component of the set Fix(f), then H is smooth, irreducible and H = Fix(f) and for K = C the Euler characteristic of H is equal to 1.
Keywords
Cite
@article{arxiv.1409.7883,
title = {On the set of fixed points of a polynomial automorphism},
author = {Zbigniew Jelonek and Tomasz Lenarcik},
journal= {arXiv preprint arXiv:1409.7883},
year = {2014}
}