Stabilization of monomial maps in higher codimension
Journal article, 2014

A monomial self-map $f$ on a complex toric variety is said to be $k$-stable if the action induced on the $2k$-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 $k$-stable. If $f$ is replaced by an iterate one can find a $k$-stable model as soon as the dynamical degrees $\lambda _k$ of $f$ satisfy $\lambda _k^2>\lambda _{k-1}\lambda _{k+1}$. On the other hand, we give examples of monomial maps $f$, where this condition is not satisfied and where the degree sequences $\deg _k(f^n)$ do not satisfy any linear recurrence. It follows that such an $f$ is not $k$-stable on any toric model with at worst quotient singularities.

degree growth

monomial maps

Algebraic stability


Jan-Li Lin

Elizabeth Wulcan

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Annales de lInstitut Fourier

0373-0956 (ISSN)

Vol. 64 5 2127-2146

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Basic sciences



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