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Dynamical invariants of monomial correspondences

Part of:Complex dynamical systemsSpecial varietiesCurvesProjective and enumerative geometry

Published online by Cambridge University Press:  02 June 2020

NGUYEN-BAC DANG and
ROHINI RAMADAS
NGUYEN-BAC DANG
Affiliation:
Stony Brook University, Institute of Mathematical Sciences, Stony Brook, NY 11794, USA email nguyen-bac.dang@stonybrook.edu
ROHINI RAMADAS
Affiliation:
Brown University, 219 Kassar House, 151 Thayer Street, Providence, RI 02912, USA email rohini_ramadas@brown.edu
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Abstract

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We focus on various dynamical invariants associated to monomial correspondences on toric varieties, using algebraic and arithmetic geometry. We find a formula for their dynamical degrees, relate the exponential growth of the degree sequences to a strict log-concavity condition on the dynamical degrees and compute the asymptotic rate of the growth of heights of points of such correspondences.

Keywords

arithmetic and algebraic dynamicsmonomial correspondancesdynamical degrees

MSC classification

Primary:14H10: Families, moduli (algebraic)
Secondary:14N99: None of the above, but in this section14M99: None of the above, but in this section37F05: Relations and correspondences

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 7 , July 2021, pp. 2000 - 2015
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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