Higher arithmetic degrees of dominant rational self-maps

Nguyen Bac Dang, Dragos Ghioca, Fei Hu, John Lesieutre, Matthew Satriano

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Suppose that f W X 99K X is a dominant rational self-map of a smooth projective variety defined over Q. Kawaguchi and Silverman conjectured that if P 2 X.Q/ is a point with well-defined forward orbit, then the growth rate of the height along the orbit exists, and coincides with the first dynamical degree !1.f / of f if the orbit of P is Zariski dense in X. In this note, we extend the Kawaguchi-Silverman conjecture to the setting of orbits of higher-dimensional subvarieties of X. We begin by defining a set of arithmetic degrees of f , independent of the choice of cycles, and we then develop the theory of arithmetic degrees in parallel to existing results for dynamical degrees. We formulate several conjectures governing these higher arithmetic degrees, relating them to dynamical degrees.

Original languageEnglish (US)
Pages (from-to)463-481
Number of pages19
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Volume23
Issue number1
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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