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math.AG2018
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…
math.AG2018
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…
math.AG2018
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…