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

TL;DR

This paper proves the effectiveness of dynatomic cycles in identifying periodic points of morphisms on projective varieties by employing deformation theory techniques.

Contribution

It introduces a deformation theory approach to establish the effectivity of dynatomic cycles for morphisms of projective varieties, advancing the understanding of periodic points.

Findings

Dynatomic cycles are effective for morphisms of projective varieties.

Deformation theory provides a new proof of dynatomic cycle effectivity.

The method helps identify formal periodic points in algebraic dynamics.

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.