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Non-thin rational points for elliptic K3 surfaces
Damián Gvirtz-Chen, Giacomo Mezzedimi
We prove that elliptic K3 surfaces over a number field which admit a second elliptic fibration satisfy the potential Hilbert property. Equivalently, the set of their rational point…
Surfaces defined by pairs of polynomials
Damián Gvirtz-Chen, Alexei Skorobogatov
We prove that the Brauer group of the generic diagonal surface of arbitrary degree is trivial. The same method is applied to surfaces whose equation can be written as the sum of tw…
A Hilbert Irreducibility Theorem for Enriques surfaces
Damián Gvirtz-Chen, Giacomo Mezzedimi
We define the over-exceptional lattice of a minimal algebraic surface of Kodaira dimension 0. Bounding the rank of this object, we prove that a conjecture by Campana and Corvaja--Z…
Mazur's Conjecture and An Unexpected Rational Curve on Kummer Surfaces and their Superelliptic Generalisations
Damián Gvirtz-Chen
We prove the following special case of Mazur's conjecture on the topology of rational points. Let be an elliptic curve over with -invariant . For a class…
Arithmetic Surjectivity for Zero-Cycles
Damián Gvirtz-Chen
Let be a proper, dominant morphism of smooth varieties over a number field . When is it true that for almost all places of , the fibre over any point $P\…