54 citations · 142 across the 14 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…
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…