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 …

In these lecture notes we give an introduction to Bridgeland stability conditions on smooth
complex projective varieties with a particular focus on the case of surfaces. This includes …

Let Y d be a del Pezzo threefold of Picard rank one and degree d≥ 2. In this paper, we
apply two different viewpoints to study Y d via a particular admissible subcategory of its …

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 …

For various 2-Calabi-Yau categories $\mathscr {C} $ for which the stack of objects
$\mathfrak {M} $ has a good moduli space $ p\colon\mathfrak {M}\rightarrow\mathcal {M} …

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 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 …

Using the technique of categorical absorption of singularities we prove that the nontrivial
components of the derived categories of del Pezzo threefolds of degree\(d\in\{2, 3, 4, 5\}\) …