K3 surfaces are central objects in modern algebraic geometry. This book examines this
important class of Calabi–Yau manifolds from various perspectives in eighteen self …

We construct a family of nef divisor classes on every moduli space of stable complexes in
the sense of Bridgeland. This divisor class varies naturally with the Bridgeland stability …

This paper surveys the recent advances concerning the relations between triangulated (or
derived) categories and their dg enhancements. We explain when some interesting …

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 …

Abstract Let X→ Y be a fibration whose fibers are complete intersections of r quadrics. We
develop new categorical and algebraic tools—a theory of relative homological projective …

We prove a general criterion that guarantees that an admissible subcategory KK of the
derived category of an abelian category is equivalent to the bounded derived category of the …

We survey some recent results concerning the so called Categorical Torelli problem. This is
to say how one can reconstruct a smooth projective variety up to isomorphism, by using the …

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This paper surveys some recent results about Fourier--Mukai functors. In particular, given an
exact functor between the bounded derived categories of coherent sheaves on two smooth …

We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a
motivic interpretation of a long standing conjecture of Šafarevic which has been settled only …