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12 papers · 1 filter
Maximal variation of curves on K3 surfaces
Yajnaseni Dutta, Daniel Huybrechts
We prove that curves in a non-primitive, base point free, ample linear system on a K3 surface have maximal variation. The result is deduced from general restriction theorems applie…
On birational transformations of Hilbert schemes of points on K3 surfaces
Pietro Beri, Alberto Cattaneo
We classify the group of birational automorphisms of Hilbert schemes of points on algebraic K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or n…
Lagrangian fibrations of hyperkähler fourfolds
Daniel Huybrechts, Chenyang Xu
The base surface of a Lagrangian fibration of a projective, irreducible symplectic fourfold is shown to be isomorphic to .
Non-symplectic involutions on manifolds of -type
Chiara Camere, Alberto Cattaneo, Andrea Cattaneo
We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a surface and admitting a non-symplectic involution. We classify t…
A case of the deformational Hodge conjecture via a pro Hochschild-Kostant-Rosenberg theorem
Matthew Morrow
Following ideas of Bloch, Esnault, and Kerz, the deformational part of Grothendieck's variational Hodge conjecture is established for proper, smooth schemes over , where $K…
Effective de Rham Cohomology - The Hypersurface Case
Peter Scheiblechner
We prove an effective bound for the degrees of generators of the algebraic de Rham cohomology of smooth affine hypersurfaces. In particular, we show that the de Rham cohomology H_d…