54 citations · 142 across the 14 of their papers we have counts for
17 papers
Explicit computation of symmetric differentials and its application to quasi-hyperbolicity
Nils Bruin, Jordan Thomas, Anthony Várilly-Alvarado
We develop explicit techniques to investigate algebraic quasi-hyperbolicity of singular surfaces through the constraints imposed by symmetric differentials. We apply these methods…
Locally recoverable codes on surfaces
Cecília Salgado, Anthony Várilly-Alvarado, José Felipe Voloch
A linear error correcting code is a subspace of a finite-dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with lo…
Campana points of bounded height on vector group compactifications
Marta Pieropan, Arne Smeets, Sho Tanimoto +1
We initiate a systematic quantitative study of subsets of rational points that are integral with respect to a weighted boundary divisor on Fano orbifolds. We call the points in the…
Odd order obstructions to the Hasse principle on general K3 surfaces
Jennifer Berg, Anthony Várilly-Alvarado
We show that odd order transcendental elements of the Brauer group of a K3 surface can obstruct the Hasse principle. We exhibit a general K3 surface of degree 2 over $\mathbb{Q…
Campana points, Vojta's conjecture, and level structures on semistable abelian varieties
Dan Abramovich, Anthony Várilly-Alvarado
We introduce a qualitative conjecture, in the spirit of Campana, to the effect that certain subsets of rational points on a variety over a number field, or a Deligne-Mumford stack…
Abelian -division fields of elliptic curves and Brauer groups of product Kummer & abelian surfaces
Anthony Várilly-Alvarado, Bianca Viray
Let be a principal homogeneous space of an abelian surface, or a K3 surface, over a finitely generated extension of . In 2008, Skorobogatov and Zarhin showed that t…
Level structures on abelian varieties, Kodaira dimensions, and Lang's conjecture
Dan Abramovich, Anthony Várilly-Alvarado
Assuming Lang's conjecture, we prove that for a fixed prime , number field , and positive integer , there is an integer such that no principally polarized abelian vari…
Kodaira dimension of moduli of special cubic fourfolds
Sho Tanimoto, Anthony Várilly-Alvarado
A special cubic fourfold is a smooth hypersurface of degree three and dimension four that contains a surface not homologous to a complete intersection. Special cubic fourfolds give…
Brauer groups on K3 surfaces and arithmetic applications
Kelly McKinnie, Justin Sawon, Sho Tanimoto +1
For a prime , we study subgroups of order p of the Brauer group Br(S) of a general complex polarized K3 surface of degree 2d, generalizing earlier work of van Geemen. These grou…
Vertical Brauer groups and del Pezzo surfaces of degree 4
Anthony Várilly-Alvarado, Bianca Viray
We show that Brauer classes of a locally solvable degree 4 del Pezzo surface X are vertical for some projection away from a plane f: X ---> P^1, i.e., that every Brauer class is ob…
Cubic fourfolds containing a plane and a quintic del Pezzo surface
Asher Auel, Marcello Bernardara, Michele Bolognesi +1
We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontr…
Failure of the Hasse principle for Enriques surfaces
Anthony Várilly-Alvarado, Bianca Viray
We construct an Enriques surface X over Q with empty étale-Brauer set (and hence no rational points) for which there is no algebraic Brauer-Manin obstruction to the Hasse principle…
Transcendental obstructions to weak approximation on general K3 surfaces
Brendan Hassett, Anthony Várilly-Alvarado, Patrick Varilly
We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental Brauer-Manin obstruction to weak…
Density of rational points on isotrivial rational elliptic surfaces
Anthony Várilly-Alvarado
For a large class of isotrivial rational elliptic surfaces (with section), we show that the set of rational points is dense for the Zariski topology, by carefully studying variatio…
Arithmetic E_8 lattices with maximal Galois action
Anthony Várilly-Alvarado, David Zywina
We construct explicit examples of E_8 lattices occurring in arithmetic for which the natural Galois action is equal to the full group of automorphisms of the lattice, i.e., the Wey…
Cox rings of degree one del Pezzo surfaces
Damiano Testa, Anthony Várilly-Alvarado, Mauricio Velasco
Let X be a del Pezzo surface of degree one over an algebraically closed field (of any characteristic), and let Cox(X) be its total coordinate ring. We prove the missing case of a c…
Weak approximation on del Pezzo surfaces of degree 1
Anthony Várilly-Alvarado
We study del Pezzo surfaces of degree 1 of the form w^2 = z^3 + Ax^6 + By^6 in the weighted projective space P_k(1,1,2,3), where k is a perfect field of characteristic not 2 or 3 a…