64 citations · 233 across the 33 of their papers we have counts for
32 papers · 1 filter
Numerical invariants of hyper-Kähler manifolds
Olivier Debarre, Chen Jiang
We study various constraints on the Beauville quadratic form and the Huybrechts-Riemann-Roch polynomial for hyper-Kähler manifolds, mostly in dimension 6 and in the presence of an…
Quadrics on Gushel-Mukai varieties
Olivier Debarre, Alexander Kuznetsov
We study Hilbert schemes of quadrics of dimension on smooth Gushel-Mukai varieties of dimension by relating them to the relative Hilbe…
Smooth subvarieties of Jacobians
Olivier Benoist, Olivier Debarre
We give new examples of algebraic integral cohomology classes on smooth projective complex varieties that are not integral linear combinations of classes of smooth subvarieties. So…
Computing Riemann-Roch polynomials and classifying hyper-Kähler fourfolds
Olivier Debarre, Daniel Huybrechts, Emanuele Macrì +1
We prove that a hyper-Kähler fourfold satisfying a mild topological assumption is of K3 deformation type. This proves in particular a conjecture of O'Grady stating that hyp…
Complete curves in the moduli space of polarized K3 surfaces and hyper-Kähler manifolds
Olivier Debarre, Emanuele Macrì
Building on an idea of Borcherds, Katzarkov, Pantev, and Shepherd-Barron (who treated the case ), we prove that the moduli space of polarized K3 surfaces of degree conta…
Gushel-Mukai varieties with many symmetries and an explicit irrational Gushel-Mukai threefold
Olivier Debarre, Giovanni Mongardi
We construct an explicit complex smooth Fano threefold with Picard number 1, index 1, and degree 10 (also known as a Gushel-Mukai threefold) and prove that it is not rational by sh…
Gushel--Mukai varieties: intermediate Jacobians
Olivier Debarre, Alexander Kuznetsov
We describe intermediate Jacobians of Gushel-Mukai varieties of dimensions 3 or 5: if is the Lagrangian space associated with , we prove that the intermediate Jacobian o…
Gushel-Mukai varieties
Olivier Debarre
Gushel-Mukai varieties are smooth complex dimensionally transverse intersections of a cone over the Grassmannian with a linear space and a quadratic hypersurface…
Hilbert squares of K3 surfaces and Debarre-Voisin varieties
Olivier Debarre, Frédéric Han, Kieran O'Grady +1
The Debarre-Voisin hyperkähler fourfolds are built from alternating -forms on a -dimensional complex vector space, which we call trivectors. They are analogous to the Beauvi…
Gushel-Mukai varieties: moduli
Olivier Debarre, Alexander Kuznetsov
We describe the moduli stack of Gushel-Mukai varieties as a global quotient stack and its coarse moduli space as the corresponding GIT quotient. The construction is based on a comp…
Hyperkähler manifolds
Olivier Debarre
The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperkähler manifolds. Thes…
Double covers of quadratic degeneracy and Lagrangian intersection loci
Olivier Debarre, Alexander Kuznetsov
We explain a general construction of double covers of quadratic degeneracy loci and Lagrangian intersection loci based on reflexive sheaves. We relate the double covers of quadrati…
On the period map for polarized hyperkähler fourfolds
Olivier Debarre, Emanuele Macrì
This is an improved version of the eprint previously entitled "Unexpected isomorphisms between hyperkähler fourfolds." We study smooth projective hyperkähler fourfolds that are def…
On the cohomology of Gushel-Mukai sixfolds
Olivier Debarre, Alexander Kuznetsov
We provide a stable rationality construction for some smooth complex Gushel-Mukai varieties of dimension 6. As a consequence, we compute the integral singular cohomology of any smo…
Gushel-Mukai varieties: linear spaces and periods
Olivier Debarre, Alexander Kuznetsov
Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic fourfold and the primitive second cohomology of its variety of lines, a smooth hy…
Cohomological characterizations of the complex projective space
Olivier Debarre
In this survey, we discuss whether the complex projective space can be characterized by its integral cohomology ring among compact complex manifolds.
Lines on cubic hypersurfaces over finite fields
Olivier Debarre, Antonio Laface, Xavier Roulleau
We show that smooth cubic hypersurfaces of dimension defined over a finite field contain a line defined over in each of the following cases: - and…
Gushel--Mukai varieties: classification and birationalities
Olivier Debarre, Alexander Kuznetsov
We perform a systematic study of Gushel-Mukai varieties---quadratic sections of linear sections of cones over the Grassmannian Gr(2,5). This class of varieties includes Clifford ge…
Rational cohomology tori
Olivier Debarre, Zhi Jiang, Martí Lahoz +1
We study normal compact Kähler spaces whose rational cohomology ring is isomorphic to that of a complex torus. We call them rational cohomology tori. We classify, up to dimension t…
Monomial transformations of the projective space
Olivier Debarre, Bodo Lass
We prove that, over any field, the dimension of the indeterminacy locus of a rational transformation of which is defined by monomials of the same degree with no commo…
Pseudo-effective classes and pushforwards
O. Debarre, Z. Jiang, C. Voisin
Given a morphism between complex projective varieties, we make several conjectures on the relations between the set of pseudo-effective (co)homology classes which are annihilated b…
Special prime Fano fourfolds of degree 10 and index 2
Olivier Debarre, Atanas Iliev, Laurent Manivel
Mukai proved that most prime Fano fourfolds of degree 10 and index 2 are contained in a Grassmannian G(2,5). They are all unirational and some are rational, as remarked by Roth in…
Varieties with vanishing holomorphic Euler characteristic
J. A. Chen, O. Debarre, Z. Jiang
We study smooth complex projective varieties of maximal Albanese dimension and of general type satisfying with vanishing holomorphic Euler characteristic. We prove that the Alb…
On nodal prime Fano threefolds of degree 10
Olivier Debarre, Atanas Iliev, Laurent Manivel
We study the geometry and the period map of nodal complex prime Fano threefolds with index 1 and degree 10. We show that these threefolds are birationally isomorphic to Verra solid…