相关论文: HyperK\"ahler Manifolds and Birational Transformat…

This paper deals with rational curves and birational contractions on irreducible holomorphically symplectic manifold. We survey some recent results about minimal rational curves, their deformations, extremal rays associated with these…

In this paper we analyse the birational geometry of O'Grady ten dimensional manifolds, giving a characterisation of Kaehler classes and lagrangian fibrations. Moreover, we study symplectic compactifications of intermediate jacobian…

Any minimal model of a projective Hyperkaehler manifold is a projective Hyperkaehler manifold. As a consequence, moduli spaces of sheaves on a k3 that don't admit a symplectic resolution are not birational to Hyperkaehler manifolds.

The known counterexamples to the global Torelli theorem for higher-dimensional hyperkahler manifolds are provided by birational manifolds. We address the question whether two birational hyperkahler manifolds (i.e. irreducible symplectic)…

We show that any birational map between projective hyperK\"ahler manifolds of dimension 4 is composed of a sequence of simple flops or elementary Mukai transformations under the assumption that each irreducible component of the…

In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective…

This is a survey on symplectic birational geometry. In arbitrary dimension, this subject is centered around the notion of uniruledness. In low dimensions, we will also discuss Kodaira dimension and minimality.

Our aim is to illustrate how one can effectively apply the basic ideas and notions of topological entropy and dynamical degrees, together with recent progress of minimal model theory in higher dimension, for an explicit study of birational…

We study the behavior of birational automorphism groups in families of projective hyper-K\"ahler manifolds.

This is an attempt towards the understanding of the (birational) Kaehler cone of a compact hyperkaehler manifold in terms of the Beauville-Bogomolov form on its second cohomology. We discuss birational correspondences between hyperkaehler…

We study smooth projective varieties with small dual variety using methods from symplectic topology. We prove the affine parts of such varieties are subcritical, and that the hyperplane class is invertible in their quantum cohomology. We…

In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.

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 non-symplectic and if there exists a hyperk\"ahler birational…

We survey our recent papers (some being joint ones) about the relation between the geometry of a compact K\"ahler manifold and the existence of automorphisms of positive entropy on it. We also use the language of log minimal model program…

We survey and explain some recent work at the intersection of model theory and bimeromorphic geometry (classification of compact complex manifolds). Included here are the essential saturation of the many sorted structure $\mathcal{C}$ of…

We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the K\"ahler geometry of a finite dimensional complex projective spaces.

Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are bi-Lagrangian and that they are obtained by complex submanifolds via…

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many…

We give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.

A locally conformally K\"ahler (LCK) manifold is a complex manifold $M$ which has a K\"ahler structure on its cover, such that the deck transform group acts on it by homotheties. Assume that the K\"ahler form is exact on the minimal…