64 citations · 184 across the 8 of their papers we have counts for
9 papers
Geometric realizations of Brauer classes on K3 surfaces from hyperkähler contractions
Sarah Frei, Jack Petok, Anthony Várilly-Alvarado
Elements of the Brauer group of a variety have geometric incarnations as étale-projective -bundles, yet producing minimalist constructions of such bun…
Reduction of Brauer classes on K3 surfaces, rationality and derived equivalence
Sarah Frei, Brendan Hassett, Anthony Várilly-Alvarado
We consider the reduction of Brauer classes on surfaces over number fields, with a view toward applications to rationality and derived equivalence. We show that a Brauer class on a…
Locally recoverable codes from algebraic curves and surfaces
Alexander Barg, Kathryn Haymaker, Everett W. Howe +2
A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other c…
Cubic fourfolds fibered in sextic del Pezzo surfaces
Nicolas Addington, Brendan Hassett, Yuri Tschinkel +1
We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimension-two subvarieties in the moduli space. Our examples are fibered in sex…
Level structures on abelian varieties and Vojta's conjecture
Dan Abramovich, Keerthi Madapusi Pera, Anthony Várilly-Alvarado
Assuming Vojta's conjecture, and building on recent work of the authors, we prove that, for a fixed number field and positive integer , there is an integer such that f…
On the Unirationality of del Pezzo surfaces of degree two
Cecília Salgado, Damiano Testa, Anthony Várilly-Alvarado
Among geometrically rational surfaces, del Pezzo surfaces of degree two over a field k containing at least one point are arguably the simplest that are not known to be unirational…
Failure of the Hasse principle on general K3 surfaces
Brendan Hassett, Anthony Várilly-Alvarado
We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general K3 surface X of degree 2 over Q, together…
Laurent polynomials and Eulerian numbers
Daniel Erman, Gregory G. Smith, Anthony Várilly-Alvarado
Duistermaat and van der Kallen show that there is no nontrivial complex Laurent polynomial all of whose powers have a zero constant term. Inspired by this, Sturmfels posed two ques…
Big rational surfaces
Damiano Testa, Anthony Várilly-Alvarado, Mauricio Velasco
We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of the plane at dist…