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The theorem of Maehara-Severi for maps of general type
Finn Bartsch, Ariyan Javanpeykar, Erwan Rousseau
We prove a finiteness result for dominant rational maps whose orbifold base is of general type. Our finiteness result generalizes Maehara's theorem that a given variety dominates o…
Weakly special varieties, Campana stacks, and Remarks on Orbifold Mordell
Finn Bartsch, Ariyan Javanpeykar
We construct the first weakly special surfaces that are not Campana-special, including the complement of the plane curve in . We prove that the set of $\…
The map to the orbifold base need not be an orbifold map
Finn Bartsch
We give an explicit example of a fibration between smooth projective varieties whose "orbifold base" in the sense of Campana has the property that the indu…
More counterexamples to the Arithmetic Puncturing Problem
Finn Bartsch
We construct examples of threefolds with terminal singularities (resp. surfaces with canonical singularities) which are special in the sense of Campana, have a potentially dense se…
The Kobayashi pseudometric in the presence of log-terminal singularities
Finn Bartsch
We show that the Kobayashi pseudometric is well-behaved under resolution of log-terminal singularities. This answers a question of Kamenova and Lehn.
On the finiteness of maps into simple abelian varieties satisfying certain tangency conditions
Finn Bartsch
We show that given a simple abelian variety and a normal variety defined over a finitely generated field of characteristic zero, the set of non-constant morphisms $V \t…
New examples of geometrically special varieties: K3 surfaces, Enriques surfaces, and algebraic groups
Finn Bartsch
We verify that elliptic K3 surfaces and algebraic groups have many rational points over function fields, i.e., they are geometrically special in the sense of Javanpeykar-Rousseau.…
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…
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…
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…
Weakly-special threefolds and non-density of rational points
Finn Bartsch, Ariyan Javanpeykar, Erwan Rousseau
We verify part of a conjecture of Campana predicting that rational points on the weakly-special non-special simply-connected smooth projective threefolds constructed by Bogomolov-T…