11 citations · 44 across the 13 of their papers we have counts for
17 papers
Equivariant Unirationality of Cubic Threefolds
Matthew Ballard, Alexander Duncan, Zhijia Zhang
Using the recent proof of the Cassels--Swinnerton-Dyer conjecture for cubic surfaces, we finish the classification of -unirational complex cubic threefolds. In particular, we pr…
Consequences of the existence of exceptional collections in arithmetic and rationality
Matthew R. Ballard, Alexander Duncan, Alicia Lamarche +1
A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic…
Separable algebras and coflasque resolutions
Matthew R. Ballard, Alexander Duncan, Alicia Lamarche +1
Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects. The most famous example is the deep connect…
Birational self-maps of threefolds of (un)-bounded genus or gonality
Jérémy Blanc, Ivan Cheltsov, Alexander Duncan +1
We study the complexity of birational self-maps of a projective threefold by looking at the birational type of surfaces contracted. These surfaces are birational to the product…
Derived categories of centrally-symmetric smooth toric Fano varieties
Matthew R Ballard, Alexander Duncan, Patrick K. McFaddin
We exhibit full exceptional collections of vector bundles on any smooth, Fano arithmetic toric variety whose split fan is centrally symmetric.
Finite quasisimple groups acting on rationally connected threefolds
Jérémy Blanc, Ivan Cheltsov, Alexander Duncan +1
We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: , $\operatorname{P…