54 citations · 385 across the 62 of their papers we have counts for
6 papers · 2 filters
Cremona transformations and derived equivalences of K3 surfaces
Brendan Hassett, Kuan-Wen Lai
We exhibit a Cremona transformation of such that the base loci of the map and its inverse are birational to K3 surfaces. The two K3 surfaces are derived equivalent but…
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…
A very general quartic double fourfold is not stably rational
Brendan Hassett, Alena Pirutka, Yuri Tschinkel
We prove that a very general double cover of the projective four-space, ramified in a quartic threefold, is not stably rational.
Stable rationality of quadric surface bundles over surfaces
Brendan Hassett, Alena Pirutka, Yuri Tschinkel
We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases,…
On stable rationality of Fano threefolds and del Pezzo fibrations
Brendan Hassett, Yuri Tschinkel
We prove that very general non-rational Fano threefolds which are not birational to cubic threefolds are not stably rational.
Cubic fourfolds, K3 surfaces, and rationality questions
Brendan Hassett
This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures…