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 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 study moduli spaces of stable objects in Enriques categories by exploiting their relation
to moduli spaces of stable objects in associated K3 categories. In particular, we settle 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 settle the last open case of Kuznetsov's conjecture on the derived categories of Fano
threefolds. Contrary to the original conjecture, we prove the Kuznetsov components of …

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 …

This work establishes a condition that determines when strong generation in the bounded
derived category of a Noetherian J-2 scheme is preserved by the derived pushforward of a …

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 …

We show that the stability conditions on the Kuznetsov component of a Gushel–Mukai
threefold, constructed by Bayer, Lahoz, Macrì and Stellari, are preserved by the Serre …

arXiv:2109.13549v4 [math.AG] 24 Jan 2023 Page 1 Épijournal de Géométrie Algébrique
epiga.episciences.org Volume 7 (2023), Article No. 1 Serre-invariant stability conditions and …