Göteborgs universitets publikationer

# Stabilization of monomial maps in higher codimension

## Stabilisation des applications monomiales en haute codimension

Författare och institution:
Jan-Li Lin (-); Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Annales de l'Institut Fourier, 64 ( 5 ) s. 2127-2146
ISSN:
0373-0956
E-ISSN:
1777-5310
Antal sidor:
14
Publikationstyp:
Publiceringsår:
2014
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
Algebraic stability; monomial maps; degree growth
Chalmers fundament:
Grundläggande vetenskaper
Postens nummer:
167593