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math.AG2025
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…
math.AG2025
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…
math.AG2024
Intersection of orbits of loxodromic automorphisms of affine surfaces
Marc Abboud
We show the following result: If is an affine surface over a field and are two loxodromic automorphisms with an orbit meeting infinitely many times, then and $…