Keiji Oguiso

Autoequivalences of derived category of a K3 surface and monodromy transformations

We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge isometries of the Mukai lattice. Motivated by homological mirror symmetry we also consider the mirror counterpart, i.e. symplectic version of it. In the case of ρ(X) = 1, we find an explicit formula which reproduces the number of Fourier-Mukai (FM) partners from the monodromy problem of the mirror K3 family. We present an explicit example in which a monodromy action does not come from an autoequivalence of the mirror side.

On Vorontsov's Theorem on K3 surfaces with non-symplectic group actions

We shall give a proof for Vorontsov’s Theorem and apply this to classify log Enriques surfaces with large prime canonical index.

THE SIMPLE GROUP OF ORDER 168 AND K3 SURFACES

The aim of this note is to characterize a K3 surface of Klein-Mukai type in terms of its symmetry.

Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups

Thanks to the theory of Coxeter groups, we produce the first family of Calabi-Yau manifolds

Characteristic foliation on the discriminant hypersurface of a holomorphic Lagrangian fibration

X

The Alternating Group of Degree 6 in the Geometry of the Leech Lattice and K3 Surfaces

of arbitrary dimension

A characterization of the Fermat quartic K3 surface by means of finite symmetries

n

c = 2 Rational Toroidal Conformal Field Theories via the Gauss Product

, for which

Automorphisms of Elliptic K3 surfaces and Salem numbers of maximal degree

{\rm Bir}(X)

Extensions of the alternating group of degree 6 in the geometry of K3 surfaces

is infinite and the Kawamata-Morrison movable cone conjecture is satisfied. For this family, the movable cone is explicitly described; its fractal nature is related to limit sets of Kleinian groups and to the Apollonian Gasket. Then, we produce explicit examples of (biregular) automorphisms with positive entropy on some Calabi-Yau varieties.