26 citations · 97 across the 17 of their papers we have counts for
25 papers
Very general quartic sixfolds are not stably rational
John Christian Ottem
We prove that a very general quartic sixfold admits no decomposition of the diagonal, and in particular is not stably rational. The proof uses specialization to an explicit quartic…
Fano varieties with torsion in the third cohomology group
John Christian Ottem, Jørgen Vold Rennemo
We construct first examples of Fano varieties with torsion in their third cohomology group. The examples are constructed as double covers of linear sections of rank loci of symmetr…
Planes in cubic fourfolds
Alex Degtyarev, Ilia Itenberg, John Christian Ottem
We show that the maximal number of planes in a complex smooth cubic fourfold in is , realized by the Fermat cubic only; the maximal number of real planes in a…
A refinement of the motivic volume, and specialization of birational types
Johannes Nicaise, John Christian Ottem
We construct an upgrade of the motivic volume by keeping track of dimensions in the Grothendieck ring of varieties. This produces a uniform refinement of the motivic volume and its…
Two coniveau filtrations
Olivier Benoist, John Christian Ottem
A cohomology class of a smooth complex variety of dimension has coniveau if it vanishes in the complement of a closed subvariety of codimension , and has stron…
Tropical degenerations and stable rationality
Johannes Nicaise, John Christian Ottem
We use the motivic obstruction to stable rationality introduced by Shinder and the first-named author to establish several new classes of stably irrational hypersurfaces and comple…
A pencil of Enriques surfaces with non-algebraic integral Hodge classes
John Christian Ottem, Fumiaki Suzuki
We prove that there exists a pencil of Enriques surfaces defined over with non-algebraic integral Hodge classes of non-torsion type. This gives the first example of a…
On deformations of quintic and septic hypersurfaces
John Christian Ottem, Stefan Schreieder
An old question of Mori asks whether in dimension at least three, any smooth specialization of a hypersurface of prime degree is again a hypersurface. A positive answer to this que…
Remarks on the positivity of the cotangent bundle of a K3 surface
Frank Gounelas, John Christian Ottem
Using recent results of Bayer-Macrì, we compute in many cases the pseudoeffective and nef cones of the projectivised cotangent bundle of a smooth projective K3 surface. We then use…
Curve classes on irreducible holomorphic symplectic varieties
Giovanni Mongardi, John Christian Ottem
We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give…
Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero
Olivier Benoist, John Christian Ottem
We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first e…
Positivity of the diagonal
Brian Lehmann, John Christian Ottem
We study how the geometry of a projective variety is reflected in the positivity properties of the diagonal considered as a cycle on . We analyze when the dia…
A counterexample to the birational Torelli problem for Calabi-Yau threefolds
John Christian Ottem, Jørgen Vold Rennemo
The Grassmannian Gr(2,5) is embedded in via the Plücker embedding. The intersection of two general PGL(10)-translates of Gr(2,5) is a Calabi-Yau 3-fold X, and the inter…
Effective cones of cycles on blow-ups of projective space
Izzet Coskun, John Lesieutre, John Christian Ottem
In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blow-ups of projective space. We determine bounds on the number of points for which these…
Nef cycles on some hyperkahler fourfolds
John Christian Ottem
We study the cones of surfaces on varieties of lines on cubic fourfolds and Hilbert schemes of points on K3 surfaces. From this we obtain new examples of nef cycles which fail to b…
Curves disjoint from a nef divisor
John Lesieutre, John Christian Ottem
On a projective surface it is well-known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimensi…
Quartic Spectrahedra
John Christian Ottem, Kristian Ranestad, Bernd Sturmfels +1
Quartic spectrahedra in 3-space form a semialgebraic set of dimension 24. This set is stratified by the location of its ten nodes. There are twenty maximal strata, identified recen…
On subvarieties with ample normal bundle
John Christian Ottem
We show that a pseudoeffective R-divisor has numerical dimension 0 if it is numerically trivial on a subvariety with ample normal bundle. This implies that the cycle class of a cur…
Birational geometry of hypersurfaces in products of projective spaces
John Christian Ottem
We study the birational properties of hypersurfaces in products of projective spaces. In the case of hypersurfaces in P^m x P^n, we describe their nef, movable and effective cones…
Components of the Hilbert scheme of space curves on low-degree smooth surfaces
Jan O. Kleppe, John C. Ottem
We study maximal families W of the Hilbert scheme, H(d,g)_{sc}, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on…
Partially ample line bundles on toric varieties
Nathan Broomhead, John Christian Ottem, Artie Prendergast-Smith
In this note we study properties of partially ample line bundles on simplicial projective toric varieties. We prove that the cone of q-ample line bundles is a union of rational pol…
Algebraic boundaries of Hilbert's SOS cones
Grigoriy Blekherman, Jonathan Hauenstein, John Christian Ottem +2
We study the geometry underlying the difference between non-negative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and qu…
Ample subvarieties and q-ample divisors
John Christian Ottem
We introduce a notion of ampleness for subschemes of higher codimension using the theory of q-ample line bundles. We also investigate certain geometric properties satisfied by ampl…
Cox rings of K3 surfaces with Picard number two
John Christian Ottem
We study generators and relations of Cox rings of K3 surfaces of Picard number two. In particular we consider the Cox rings of classical examples of K3 surfaces, such as quartic su…