We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite
union of codimen\-sion-two subvarieties in the moduli space. Our examples are fibered in …

We report on progress in the qualitative study of rational points on rationally connected
varieties over number fields, also examining integral points, zero-cycles, and non-rationally …

A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains
a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a …

Let Y be a principal homogeneous space of an abelian surface, or a K3 surface, over a
finitely generated extension of Q. In 2008, Skorobogatov and Zarhin showed that the Brauer …

Rational Points on K3 Surfaces and Derived Equivalence Page 1 Rational Points on K3
Surfaces and Derived Equivalence Brendan Hassett and Yuri Tschinkel Abstract. We study K3 …

We show that a Hilbert scheme of conics on a Fano fourfold double cover of P 2× P 2
ramified along a divisor of bidegree (2, 2) admits a P 1‐fibration with base being a hyper …

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 $ Y $ of degree 2 over …

We study the geometry of exceptional loci of birational contractions of hyper-Kähler fourfolds
that are of K3 [2]-type. These loci are conic bundles over K3 surfaces and we determine their …

Assuming Lang's conjecture, we prove that for a prime p, number field K, and positive
integer g, there is an integer r such that no principally polarized abelian variety A/K has full …

For the last fifteen years, numerous authors have studied the birational geometry of
projective irreducible holomorphic symplectic varieties X, seeking to relate extremal …