Mattias Jonsson
An algebraic approach to the openness conjecture of Demailly and Kollar.
Tue, 05/22/2012 - 15:01 — SomNambulAuthors: Mattias Jonsson, Mircea Mustata
Subjects: Complex Variables
AbstractWe reduce the Openness Conjecture of Demailly and Koll\'ar on the
singularities of plurisubharmonic functions to a purely algebraic statement.Dynamics on Berkovich spaces in low dimensions.
Wed, 01/11/2012 - 15:01 — SomNambulAuthors: Mattias Jonsson
Subjects: Dynamical Systems
AbstractThese are expanded lecture notes for the summer school on Berkovich spaces
that took place at the Institut de Math\'ematiques de Jussieu, Paris in 2010.
They serve to illustrate some techniques and results from the dynamics on
low-dimensional Berkovich spaces and to exhibit the structure of these spaces.Stabilization of monomial maps.
Mon, 01/25/2010 - 16:01 — SomNambulAuthors: Elizabeth Wulcan, Mattias Jonsson
Subjects: Dynamical Systems
AbstractA monomial (or 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.
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