Stabilization of monomial maps in higher codimension

Jan Li Lin, Elizabeth Wulcan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A monomial self-map f on a complex toric variety is said to be κ-stable if the action induced on the 2κ-cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of f, we can find a toric model with at worst quotient singularities where f is κ-stable. If f is replaced by an iterate one can find a k-stable model as soon as the dynamical degrees λκ of f satisfy λ2 κ2 > λκ-1λκ+1. On the other hand, we give examples of monomial maps f, where this condition is not satisfied and where the degree sequences degκ(fn) do not satisfy any linear recurrence. It follows that such an f is not κ-stable on any toric model with at worst quotient singularities.

Original languageEnglish (US)
Pages (from-to)2127-2146
Number of pages20
JournalAnnales de l'Institut Fourier
Issue number5
StatePublished - 2014


  • Algebraic stability
  • Degree growth
  • Monomial maps

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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