3 papers
math.NT2025
Galois Realisations of via non-unirational Hilbert Irreducibility
Julian Demeio, Damián Gvirtz-Chen
We establish non-unirational versions of Hilbert Irreducibility for all Hilbert modular surfaces which are of K3 type. As an application we prove new instances of the regular Inver…
math.AG2025
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…
math.NT2025
Rational curves and the Hilbert Property on Jacobian Kummer varieties
Damián Gvirtz-Chen, Zhizhong Huang
A conjecture by Corvaja and Zannier predicts that smooth, projective, simply connected varieties over a number field with Zariski dense set of rational points have the Hilbert Prop…