This is an introduction to a very active field of research, on the boundary between
mathematics and physics. It is aimed at graduate students and researchers in geometry and …

Let X and Y be smooth projective varieties over ℂ. They are called D-equivalent if their
derived categories of bounded complexes of coherent sheaves are equivalent as …

We establish a connection between smooth symplectic resolutions and symplectic
deformations of a (possibly singular) affine Poisson variety. In particular, let V be a finite …

We analyze the ample and moving cones of holomorphic symplectic manifolds, in light of
recent advances in the minimal model program. As an application, we establish a numerical …

We study smooth projective hyperkähler fourfolds that are deformations of Hilbert squares of
K3 surfaces and are equipped with a polarization of fixed degree and divisibility. They are …

Derived categories possibly give a new significant invariant for algebraic varieties. In
particular, when the canonical line bundle is trivial, there are varieties which are not …

A survey on symplectic singularities and symplectic resolutions Page 1 ANNALES
MATHÉMATIQUES BLAISE PASCAL Baohua Fu A survey on symplectic singularities and …

We prove that a hyper-Kähler fourfold satisfying a mild topological assumption is of K3
$^{[2]} $ deformation type. This proves in particular a conjecture of O'Grady stating that hyper …

We construct a new infinite family of four‐dimensional isolated symplectic singularities with
trivial local fundamental group, answering a question of Beauville raised in 2000. Three …

In this paper we study the gonality of the normalizations of curves in the linear system| H| of
a general primitively polarized complex K3 surface (S, H) of genus p. We prove two main …