Related papers: Futaki invariant for Fedosov's star products
It is shown that the normalized trace of Fedosov star product for quantum moment map depends only on the path component in the cohomology class of the symplectic form and the cohomology class of the closed formal 2-form required to define…
We study the Cahen-Gutt moment map on the space of symplectic connections of a symplectic manifold. On a K\"ahler manifold, we define a Calabi-type functional $\mathscr{F}$ on the space of K\"ahler metrics in a given K\"ahler class. We…
We show that if a compact Kaehler manifold $M$ of non-negative Ricci curvature admits closed Fedosov star product then the reduced Lie algebra of holomorphic vector fields on $M$ is reductive. This comes in pair with the obstruction…
In these notes we consider the usual Fedosov star product on a symplectic manifold $(M,\omega)$ emanating from the fibrewise Weyl product $\circ$, a symplectic torsion free connection $\nabla$ on M, a formal series $\Omega \in \nu…
In this letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differentiation. Moreover, we define the notion of a star product of Wick type on every K\"ahler manifold by a…
The notion of the Wick star-product is covariantly introduced for a general symplectic manifold equipped with two transverse polarisations. Along the lines of Fedosov method, the explicit procedure is given to construct the Wick symbols on…
In this paper, the notion of star products with separation of variables on a Kahler manifold is extended to bimodule deformations of (anti-) holomorphic vector bundles over a Kahler manifold. Here the Fedosov construction is appropriately…
We extend our investigations on $\mathfrak g$-invariant Fedosov star products and quantum momentum mappings \cite{MN03a} to star products of Wick type on pseudo-K\"ahler manifolds. Star products of Wick type can be completely characterized…
We show that there is an obstruction to the existence of a star product defined by Kontsevich graphs without directed cycles.
In this paper we construct star products on a pseudo-K\"ahler manifold $(M,\omega,I)$ using a modification of the Fedosov method based on a different fibrewise product similar to the Wick product on $\mathbb C^n$. In a first step we show…
The Futaki invariant is a fundamental tool in K\"ahler geometry representing an obstruction to the existence of K\"ahler-Einstein metrics. Recently, it was generalized to compact complex manifolds. In this paper, we prove that it vanishes…
We define a natural class of star products: those which are given by a series of bidifferential operators which at order $k$ in the deformation parameter have at most $k$ derivatives in each argument. We show that any such star product on a…
We study various aspects of Fedosov star-products on symplectic manifolds. By introducing the notion of "quantum exponential maps", we give a criterion characterizing Fedosov connections. As a consequence, a geometric realization is…
In the first part of this paper we outline the constructions and properties of Fedosov star product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and recent developments on Yau-Tian-Donaldson conjecture on…
The description of all deformation quantizations with separation of variables on a Kaehler manifold obtained in our earlier paper is used to identify the Fedosov star-product of Wick type constructed by M. Bordemann and S. Waldmann. This…
We study quantization schemes on a K\"ahler manifold and relate several interesting structures. We first construct Fedosov's star products on a K\"ahler manifold $X$ as quantizations of Kapranov's $L_\infty$-algebra structure. Then we…
We study the scalar curvature of K\"ahler metrics that have cone singularities along a divisor, with a particular focus on certain specific classes of such metrics that enjoy some curvature estimates. Our main result is that, on the…
In this paper we compute the Futaki invariant of adiabatic Kaehler classes on resolutions of Kaehler orbifolds with isolated singularities. Combined with previous existence results of extremal metrics by Arezzo-Lena-Mazzieri, this gives a…
In this paper we study the anti-integrable limit scenario of skew-product systems. We consider a generalization of such systems based on the Frenkel-Kontorova model, and prove the existence of orbits with any fibered rotation number in…
The Fedosov deformation quantization of the symplectic manifold is determined by a 1-form differential r. We identify a class of r for which the $\star$ product becomes the Moyal product by taking appropriate Darboux coordinates, but…