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# Stabilization of monomial maps in higher codimension

## Stabilisation des applications monomiales en haute codimension

Jan-Li Lin ; Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik)
Annales de l'Institut Fourier (0373-0956). Vol. 64 (2014), 5, p. 2127-2146.

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.

Nyckelord: Algebraic stability; monomial maps; degree growth

CPL Pubid: 167593

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# Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)