5 papers
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…
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…