2 citations · 9 across the 16 of their papers we have counts for
18 papers · 1 filter
Birational cubic fourfolds via an Enriques Cremona transformation
Corey Brooke, Lisa Marquand
We describe a Cremona transformation on given by the linear system of quintics that are double along the Fano model of an Enriques surface . Using this Cremona tr…
Cubic fourfolds containing highly singular hyperplane sections
Lisa Marquand, Sasha Viktorova
We construct five irreducible divisors in the moduli space of complex cubic fourfolds parametrising smooth cubic fourfolds that contain highly singular hyperplane sections. We prov…
Counting Fourier-Mukai partners of cubic fourfolds
Christian Böhning, Hans-Christian Graf von Bothmer, Lisa Marquand
We develop an algorithm to count the number of virtual Fourier-Mukai partners for a given cubic fourfold, with initial input the primitive algebraic lattice and transcendental Hodg…
Peskine sixfolds and Debarre-Voisin fourfolds with associated cubic fourfolds
Corey Brooke, Laure Flapan, Sarah Frei +1
We develop the notion of Peskine sixfolds with associated K3 surfaces and cubic fourfolds and work out numerical conditions for when these associations occur. In discriminant 24, t…
Equivariant geometry of cubic threefolds with non-isolated singularities
Ivan Cheltsov, Lisa Marquand, Yuri Tschinkel +1
We study linearizability of actions of finite groups on cubic threefolds with non-isolated singularities.
Fourier-Mukai partners of non-syzygetic cubic fourfolds and Gale duality
Christian Böhning, Hans-Christian Graf von Bothmer, Lisa Marquand
We study so-called non-syzygetic cubic fourfolds, i.e., smooth cubic fourfolds containing two cubic surface scrolls in distinct hyperplanes with intersection number between the two…
Equivariant Kuznetsov components for cubic fourfolds with a symplectic involution
Laure Flapan, Sarah Frei, Lisa Marquand
We study the equivariant Kuznetsov component of a general cubic fourfold with a symplectic involution. We show that is equivalent to the d…
Relative compactified Prym and Picard fibrations associated to very good cubic fourfolds
Yajnaseni Dutta, Lisa Marquand
A very good cubic fourfold is a smooth cubic fourfold that does not contain a plane, a cubic scroll, or a hyperplane section with a corank 3 singularity. We prove that the normaliz…
Cubic fourfolds with a symplectic automorphism of prime order
Simone Billi, Annalisa Grossi, Lisa Marquand
We determine the algebraic and transcendental lattices of a general cubic fourfold with a symplectic automorphism of prime order. We prove that cubic fourfolds admitting a symplect…
Cubic fourfolds with birational Fano varieties of lines
Corey Brooke, Sarah Frei, Lisa Marquand
We give several examples of pairs of non-isomorphic cubic fourfolds whose Fano varieties of lines are birationally equivalent (and in one example isomorphic). Two of our examples,…
Birational geometry of Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls
Corey Brooke, Sarah Frei, Lisa Marquand +1
We characterize the birational geometry of some hyperkähler fourfolds of Picard rank obtained as the Fano varieties of lines on cubic fourfolds containing pairs of cubic scroll…
Equivariant geometry of singular cubic threefolds, II
Ivan Cheltsov, Lisa Marquand, Yuri Tschinkel +1
We study linearizability of actions of finite groups on cubic threefolds with nonnodal isolated singularities.
Some density results for hyperkähler manifolds
Yajnaseni Dutta, Elham Izadi, Ljudmila Kamenova +1
Lagrangian fibrations of hyperkähler manifolds are induced by semi-ample line bundles which are isotropic with respect to the Beauville-Bogomolov-Fujiki form. For a non-isotrivial…
The defect of a cubic threefold and applications to intermediate Jacobian fibrations
Lisa Marquand, Sasha Viktorova
The defect of a cubic threefold with isolated singularities is a global invariant that measures the failure of -factoriality. We compute the defect for such cubics…
Finite groups of symplectic birational transformations of IHS manifolds of type
Lisa Marquand, Stevell Muller
We classify finite groups that act faithfully by symplectic birational transformations on an irreducible holomorphic symplectic (IHS) manifold of OG10 type. In particular, if X is…
The moduli space of cubic threefolds with a non-Eckardt type involution via intermediate Jacobians
Sebastian Casalaina-Martin, Lisa Marquand, Zheng Zhang
There are two types of involutions on a cubic threefold: the Eckardt type (which has been studied by the first named and the third named authors) and the non-Eckardt type. Here we…
Classification of Symplectic Birational Involutions of Manifolds of type
Lisa Marquand, Stevell Muller
We give a complete classification of symplectic birational involutions of manifolds of type. We approach this classification with three techniques -- via involutions of the…
Cubic Fourfolds with an Involution
Lisa Marquand
There are three types of involutions on a cubic fourfold; two of anti-symplectic type, and one symplectic. Here we show that cubics with involutions exhibit the full range of behav…