Effectivity of dynatomic cycles for morphisms of projective varieties using deformation theory

Hutz, Benjamin

doi:10.1090/S0002-9939-2012-11192-X

Effectivity of dynatomic cycles for morphisms of projective varieties using deformation theory
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Proc. Amer. Math. Soc. 140 (2012), 3507-3514 Request permission

Abstract:

Given an endomorphism of a projective variety, by intersecting the graph and the diagonal varieties we can determine the set of periodic points. In an effort to determine the periodic points of a given minimal period, we follow a construction similar to cyclotomic polynomials. The resulting zero-cycle is called a dynatomic cycle, and the points in its support are called formal periodic points. This article gives a proof of the effectivity of dynatomic cycles for morphisms of projective varieties using methods from deformation theory.

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