We develop a theory of Bridgeland stability conditions and moduli spaces of semistable
objects for a family of varieties. Our approach is based on and generalizes previous work by …

We introduce a general method to induce Bridgeland stability conditions on semiorthogonal
components of triangulated categories. In particular, we prove the existence of Bridgeland …

The aim of this introductory survey is to acquaint the reader with important objects in
complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyper …

We formulate a version of the integral Hodge conjecture for categories, prove the conjecture
for two-dimensional Calabi–Yau categories which are suitably deformation equivalent to the …

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 …

We prove that ideal sheaves of lines in a Fano three-fold of Picard rank one and index two
are stable objects in the Kuznetsov component, with respect to the stability conditions …

We prove the existence of Bridgeland stability conditions on the Kuznetsov components of
Gushel–Mukai varieties, and describe the structure of moduli spaces of Bridgeland …

We prove the generalized Franchetta conjecture for the locally complete family of hyper-
Kähler eightfolds constructed by Lehn–Lehn–Sorger–van Straten (LLSS). As a corollary, we …

For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai
vector 2 λ 1+ 2 λ 2 in the Kuznetsov component of Y. We show that with a certain choice of …