Related papers: Deformation Quantization of Kahler Manifolds

It has been shown by Claire Voisin in 2003 that one cannot always deform a compact K\"ahler manifold into a projective algebraic manifold, thereby answering negatively a question raised by Kodaira. In this article, we prove that under an…

This paper studies the quantization of the deformation of Hessian structures on a two-dimensional vector space, in the framework of Koszul-Vinberg algebras. We analyze how Hessian structures can be deformed to obtain quantum structures…

We study the space of nearly K\"{a}hler structures on compact 6-dimensional manifolds. In particular, we prove that the space of infinitesimal deformations of a strictly nearly K\"{a}hler structure (with scalar curvature scal) modulo the…

We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a…

Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_{X}$. In this paper, we study the existence of a complete scalar-flat K\"{a}hler metric on $X \setminus D$ on…

We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…

We survey some recent results and constructions of almost-K\"ahler manifolds whose curvature tensors have certain algebraic symmetries. This is an updated and corrected version of the (to be) published manuscript.

It is shown that q-deformed quantum mechanics (q-deformed Heisenberg algebra) can be interpreted as quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first-) class constraints. (Saclay, T93/027).

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.

We relate a universal formula for the deformation quantization of arbitrary Poisson structures proposed by Maxim Kontsevich to the Campbell-Baker-Hausdorff formula. Our basic thesis is that exponentiating a suitable deformation of the…

This is the first in a series of articles devoted to deformation quantization of gerbes. Here we give basic definitions and interpret deformations of a given gerbe as Maurer-Cartan elements of a differential graded Lie algebra (DGLA). We…

Quantum multiparameter deformation of real Clifford algebras is proposed. The corresponding irreducible representations are found.

In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…

We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the…

We prove that every compact K\"ahler threefold has arbitrarily small deformations to some projective manifolds, thereby solving the Kodaira problem in dimension 3.

The underlying complex structure of an ALE K\"ahler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only finitely many diffeomorphism types of minimal ALE K\"ahler…

We develop estimates for the equation of scalar curvature of singular metrics with cone angle $\beta>1$, in a big and semi-positive cohomology class on a K\"ahler manifold. We further derive the Laplacian estimate for the scalar curvature…

The aim of this paper is to classify compact Kahler manifolds with quasi-constant holomorphic sectional curvature.

This paper is concerned with the existence of constant scalar curvature Kaehler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature Kaehler metrics. We also consider the…

We demonstrate the relation between the isospectral deformation and Rieffel's deformation quantization by the action of $\mathbb{R}^d$.