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 …

We study the Clifford type inequality for a particular type of curves C_ 2, 2, 5 C 2, 2, 5, which
are contained in smooth quintic threefolds. This allows us to prove some stronger …

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

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 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 …

Motivated by results of Thurston, we prove that any autoequivalence of a triangulated
category induces a filtration by triangulated subcategories, provided the existence of …

General hyperplane sections of a Fano threefold Y of index 2 and Picard rank 1 are del
Pezzo surfaces, and their Picard group is related to a root system. To the corresponding …

In this paper, we prove a Clifford type inequality for the curve $ X_ {2, 2, 2, 4} $, which is the
intersection of a quartic and three general quadratics in $\mathbb {P}^ 5$. We thus prove a …