5 papers
The universal cover of the second-type locus of a cubic
Frank Gounelas
We prove that the surface of second-type lines on a general cubic fourfold has fundamental group of order two. Its universal cover, constructed by Huybrechts, is obtained by consid…
Isotrivial smooth curves on surfaces
Xi Chen, Frank Gounelas
We prove that a smooth projective non-uniruled surface of Picard rank one, generated by an ample and base point free line bundle, cannot be covered by an isotrivial family of smoot…
When is the diagonal contractible?
Xi Chen, Frank Gounelas
For a smooth projective complex variety , we study the problem of when there exists a birational morphism to a projective variety contracting the diagonal $…
Universal Brauer-Severi varieties
Frank Gounelas, Daniel Huybrechts
We construct universal Brauer-Severi varieties of fixed period and index and study their geometry. We determine their cohomology and their Brauer and Picard groups and show that th…
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 us…