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math.AG2024
Symmetric products and puncturing Campana-special varieties
Finn Bartsch, Ariyan Javanpeykar, Aaron Levin
We give a counterexample to the Arithmetic Puncturing Conjecture and Geometric Puncturing Conjecture of Hassett-Tschinkel using symmetric powers of uniruled surfaces, and propose a…
math.AG2024
The Weakly Special Conjecture contradicts orbifold Mordell, and hence the abc conjecture
Finn Bartsch, Frédéric Campana, Ariyan Javanpeykar +1
Starting from an Enriques surface over considered by Lafon, we give the first examples of smooth projective weakly special threefolds which fibre over the projectiv…
math.AG2024
Parshin's method and the geometric Bombieri-Lang conjecture
Finn Bartsch, Ariyan Javanpeykar
In this short survey, we explain Parshin's proof of the geometric Bombieri-Lang conjecture, and show that it can be used to give an alternative proof of Xie-Yuan's recent resolutio…