Stabilization of monomial maps
Artikel i vetenskaplig tidskrift, 2011
A monomial (i.e. equivariant) selfmap
of a toric variety is called stable
if its action on the Picard group commutes with iteration.
Generalizing work of Favre to higher dimensions,
we show that under suitable conditions,
a monomial map
can be made stable by refining the underlying fan.
In general, the resulting toric variety has quotient singularities;
in dimension two we give criteria for when it can be chosen
smooth, as well as examples when it cannot.