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Brendan Hassett

Publications and source records attributed to Brendan Hassett.

At least 19 recordsLinked to original sources
arXiv2026

Moduli of conic surfaces over the line

We study moduli spaces and monodromy groups for surfaces fibered in conics over the projective line, with a view toward explicit presentations and arithmetic applications.

math.AG↗
arXiv2024

Cubic fourfolds of discriminant 24 and rationality

Cubic fourfolds of discriminant 24 contain special codimension-two algebraic cycles of degree 6 and self-intersection 20. Such cycles may be represented by singular scrolls or del Pezzo surfaces. A discriminant 24 cubic fourfold gives rise to a twisted surface, consisting of a degree-six K3 surface and a two-torsion element of its Brauer group. We show that the cubic fourfold is rational if the Brauer class vanishes. This yields a countably-infinite collection of new examples of rational cubic fourfolds, each of codimension two in moduli.

math.AG↗
arXiv2022

Reduction of Brauer classes on K3 surfaces, rationality and derived equivalence

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 very general polarized K3 surface over a number field becomes trivial upon reduction for a set of places of positive natural density. As a consequence, there are cubic fourfolds which become rational upon reduction for a positive proportion of places, and there are twisted derived equivalent K3 surfaces which become derived equivalent upon reduction for a positive proportion of places.

math.AG↗
arXiv2022

Equivariant geometry of odd-dimensional complete intersections of two quadrics

Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating the equivariant rationality problem with analogous Diophantine questions over nonclosed fields. We explore how invariants -- both classical cohomological invariants and recent symbol constructions -- control rationality in some cases.

math.AG↗
arXiv2021

Congruent number triangles with the same hypotenuse

In this article, we discuss whether a single congruent number $t$ can have two (or more) distinct triangles with the same hypotenuse. We also describe and carry out computational experimentation providing evidence that this does not occur.

math.NT↗
arXiv2019

Cubic fourfolds fibered in sextic del Pezzo surfaces

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 sextic del Pezzo surfaces over the projective plane; they are rational whenever the fibration has a rational section.

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arXiv2019

Rationality of complete intersections of two quadrics

We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a geometrically rational threefold over a non-closed field.

math.AG↗