Szegö kernels and finite group actions

Szegö Kernels and Finite Group Actions

Let (M,ω) be a compact symplectic manifold of dimension 2n, such that [ω] ∈ H(M,Z). Fix J ∈ J (M,ω) (the contractible space of all almost complex structures on M compatible with ω), and let h and g = R(h) be the induced hermitian and riemannian structures. There exist an hermitian line bundle (A, h) on M and a unitary covariant derivative ∇A on A, such that −2πiω is the curvature of ∇A. In this...

Theta Functions and Szegö Kernels

We study relations between two fundamental constructions associated to vector bundles on a smooth complex projective curve: the theta function (a section of a line bundle on the moduli space of vector bundles) and the Szegö kernel (a section of a vector bundle on the square of the curve). Two types of relations are demonstrated. First, we establish a higher–rank version of the prime form, descr...

Moment Maps and Equivariant Szegö Kernels

Let M be a connected n-dimensional complex projective manifold and consider an Hermitian ample holomorphic line bundle (L, hL) on M . Suppose that the unique compatible covariant derivative ∇L on L has curvature −2πiΩ, where Ω is a Kähler form. Let G be a compact connected semisimple Lie group and μ : G×M → M a holomorphic Hamiltonian action on (M,Ω). Let g be the Lie algebra of G, and denote b...

Actions, Norms, Subactions and Kernels of (Fuzzy) Norms

In this paper, we introduce the notion of an action $Y_X$as a generalization of the notion of a module,and the notion of a norm $vt: Y_Xto F$, where $F$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: Y_Xto [0, 1]subseteq {bf R}$, with $bf R$  the set of all real numbers. A great many standard mappings on algebr...

Szegö Kernels for Certain Unbounded Domains