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

The starting point of this note is our recent paper with Laza and Sacc\`a on the construction of deformations of O'Grady's $10$-dimensional manifolds as compactifications of intermediate Jacobian fibrations associated to cubic fourfolds.…

We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex…

The notion of a symplectic expansion directly relates the topology of a surface to formal symplectic geometry. We give a method to construct a symplectic expansion by solving a recurrence formula given in terms of the…

We propose the definition of (twisted) generalized hyperkaehler geometry and its relation to supersymmetric non-linear sigma models. We also construct the corresponding twistor space.

We study the pseudoduality transformations in two dimensional N = (2, 2) sigma models on K\"ahler manifolds. We show that structures on the target space can be transformed into the pseudodual manifolds by means of (anti)holomorphic…

Hyperkahler quotients by non-free actions are typically highly singular, but are remarkably still partitioned into smooth hyperkahler manifolds. We show that these partitions are topological stratifications, in a strong sense. We also endow…

We call a quaternionic Kaehler manifold with non-zero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kaehler manifold. We prove that every locally symmetric…

We continue the program of Chinea, De Leon and Marrero who studied the topology of cosymplectic manifolds. We study 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kaehler structures. We show that there is…

We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.

This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.

We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved K\"ahler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex…

Here we investigate the birational geometry of projective varieties of arbitrary dimension having defective higher secant varieties. We apply the classical tool of tangential projections and we determine natural conditions for uniruledness,…

We study the geometry of exceptional loci of birational contractions of hyper-K\"ahler fourfolds that are of K3$^{[2]}$-type. These loci are conic bundles over K3 surfaces and we determine their classes in the Brauer group. For this we use…

We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical…

We construct model hyper-K\"ahler geometries that include and generalize the multi-Ooguri-Vafa model using the formalism of Gaitto, Moore, and Neitzke. This is the first paper in a series of papers making rigorous Gaiotto--Moore--Neitzke's…

A geometric triangulation of a Riemannian manifold is a triangulation where the interior of each simplex is totally geodesic. Bistellar moves are local changes to the triangulation which are higher dimensional versions of the flip operation…

We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles on hyper-K\"ahler manifolds of arbitrary dimension. In particular, we describe the DG Lie algebra controlling this deformation…

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…

This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…

In this paper, we review or introduce several differential structures on manifolds in the general setting of real and complex differential geometry, and apply this study to Teichm\"uller theory. We focus on bi-Lagrangian i.e. para-K\"ahler…