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arXiv · 1409.7883

On the set of fixed points of a polynomial automorphism

Zbigniew Jelonek·Tomasz Lenarcik
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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.

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Zbigniew Jelonek, Tomasz Lenarcik. 2014-09-28. On the set of fixed points of a polynomial automorphism. https://arxiv.org/abs/1409.7883

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