7 papers · 1 filter
Dynamical degrees of twisted rational maps
Marc Abboud, Junyi Xie
Twisted rational maps arise naturally in relative algebraic dynamics: if a rational self-map preserves a fibration, then the induced map on the generic fiber is usually not an ordi…
On the dynamics of endomorphisms of affine surfaces
Marc Abboud
In [FJ07], Favre and Jonsson developed tools from valuative theory to study the dynamics of a dominant endomorphism of the complex affine plane. We extend this theory to the case o…
A dynamical characterisation of smooth cubic affine surfaces of Markov type
Marc Abboud
Using valuative techniques, we show that a smooth affine surface with a non-elementary automorphism group and completable by a cycle of rational curves is either the algebraic toru…
Rigidity of periodic points for loxodromic automorphisms of affine surfaces
Marc Abboud
We show that two automorphisms of an affine surface with dynamical degree strictly larger than 1 share a Zariski dense set of periodic points if and only if they have the same peri…
Unlikely intersections problem for automorphisms of Markov surfaces
Marc Abboud
We study the problem of unlikely intersections for automorphisms of Markov surfaces of positive entropy. We show for certain parameters that two automorphisms with positive entropy…
A local version of the arithmetic Hodge index theorem over quasiprojective varieties
Marc Abboud
We define a local intersection number for metrised line bundles over quasiprojective varieties with compact support and show the local arithmetic Hodge index theorem for this inter…