Alessandra Sarti

A note on automorphisms and birational transformations of holomorphic symplectic manifolds

We give a necessary and sufficient condition for an automorphism of the Hilbert scheme of points on a K3 surface (non necessarily algebraic) to be induced by an automorphism of the surface. We prove furthermore that the group of birational transformations of a projective irreducible holomorphic symplectic manifold is finitely generated.

Elliptic Fibrations and Symplectic Automorphisms on K3 Surfaces

Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice U 3 ⊕ E 8(−1)2 depends only on the group but not on the K3 surface. For all the groups in the list of Nikulin we compute the invariant sublattice and its orthogonal complement by using some special elliptic K3 surfaces.

Smith theory and irreducible holomorphic symplectic manifolds

We study the cohomological properties of the fixed locus

Classification of automorphisms on a deformation family of hyper-Kähler four-folds by

X^G

p

of an automorphism group

-elementary lattices

G

PROJECTIVE MODELS OF K3 SURFACES WITH AN EVEN SET

of prime order

Kummer surfaces and K3 surfaces with

p

(\mathbb{Z} /2\mathbb{Z} )^4

acting on a variety

symplectic action

X