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 …

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 give an interpretation of the Fano variety of lines on a cubic fourfold and of the
hyperkahler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic …

We use Noether–Lefschetz theory to study the reduced Gromov–Witten invariants of a
holomorphic-symplectic variety of-type. This yields strong evidence for a new conjectural …

We give an interpretation of the Fano variety of lines on a cubic fourfold and of the
hyperkähler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic …

We study automorphisms of the Hilbert scheme of n points on a generic projective K3
surface S, for any. We show that is either trivial or generated by a non‐symplectic involution …

In analogy to the case of cubic fourfolds, we discuss the conditions under which the double
cover Y∼ A of the EPW sextic hypersurface associated to a Gushel–Mukai fourfold is …

Using the connection discovered by Hassett between the Noether-Lefschetz moduli space C
_ 42 C 42 of special cubic fourfolds of discriminant 42 and the moduli space F _ 22 F 22 of …

Gushel-Mukai varieties are smooth (complex) dimensionally transverse intersections of a
cone over the Grassmannian Gr (2, 5) with a linear space and a quadratic hypersurface …

We classify the group of birational automorphisms of Hilbert schemes of points on algebraic
K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or …