Szego Kernels and Finite Group Actions

2001/06/05 by Roberto Paoletti, Paoletti, Roberto
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.AG #math.SG

paper · pdf · doi:10.48550/arxiv.math/0106026

openalex publication_date 2001/06/05 · arxiv created 2002/07/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the context of almost complex quantization, a natural generalization of algebro-geometric linear series on a compact symplectic manifold has been proposed. Here we suppose given a compatible action of a finite group and consider the linear subseries associated to the irreducible representations of G, give conditions under which these are base-point free and study properties of the associated projective morphisms. The results obtained are new even in the complex projective case.

Citations

• Random almost holomorphic sections of ample line bundles on symplectic manifolds
• Nearly Kahlerian Embeddings of Symplectic Manifolds

Related

• The Szego kernel of a symplectic quotient
• Asymptotics of Szegö kernels under Hamiltonian torus actions
• Equivariant asymptotics of Szeg "o kernels under Hamiltonian\n SU(2)\× S¹-actions
• Equivariant Asymptotics of Szegö kernels under Hamiltonian U(2) actions
• Moment maps and equivariant Szego kernels