Effectivity of dynatomic cycles for morphisms of projective varieties using deformation theory
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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.References
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Additional Information
- Benjamin Hutz
- Affiliation: The Graduate Center, The City University of New York, New York, New York 10016
- Email: bhutz@gc.cuny.edu
- Received by editor(s): November 29, 2010
- Received by editor(s) in revised form: March 14, 2011, and April 10, 2011
- Published electronically: February 22, 2012
- Communicated by: Matthew A. Papanikolas
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3507-3514
- MSC (2010): Primary 37P35, 37P55
- DOI: https://doi.org/10.1090/S0002-9939-2012-11192-X
- MathSciNet review: 2929019