Cubic fourfolds behave in many ways like K 3 surfaces. Certain cubics—conjecturally, the
ones that are rational—have specific K 3 surfaces associated to them geometrically. Hassett …

Abstract We prove Homological Mirror Symmetry for a smooth d d-dimensional Calabi–Yau
hypersurface in projective space, for any d ≥ 3 d≥ 3 (for example, d= 3 d= 3 is the quintic …

We study the relationship between derived categories of factorizations on gauged Landau–
Ginzburg models related by variations of the linearization in Geometric Invariant Theory …

We study questions motivated by results in the classical theory of dynamical systems in the
context of triangulated and A∞-categories. First, entropy is defined for exact endofunctors …

We provide a factorization model for the continuous internal Hom, in the homotopy category
of k-linear dg-categories, between dg-categories of equivariant factorizations. This motivates …

The K3 category of a cubic fourfold Page 1 The K3 category of a cubic fourfold Daniel Huybrechts
Compositio Math. 153 (2017), 586–620. doi:10.1112/S0010437X16008137 …

We study the relationship between derived categories of factorizations on gauged Landau-
Ginzburg models related by variations of the linearization in Geometric Invariant Theory …

We introduce a new notion of commutative noetherian local rings, which we call dominant.
We explore fundamental properties of dominant local rings and compare them with other …

We prove that for any normal toric variety, the Rouquier dimension of its bounded derived
category of coherent sheaves is equal to its Krull dimension. Our proof uses the coherent …

This book is a lightly edited version of the unpublished manuscript Maximal Cohen–
Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz …