Weighted Bergman kernels on orbifolds
J. Ross, R. P. Thomas
TL;DR
This paper introduces a new notion of ampleness for line bundles on orbifolds with cyclic quotient singularities and proves an asymptotic expansion for the associated weighted Bergman kernel.
Contribution
It defines a notion of ampleness for line bundles on orbifolds and establishes a global asymptotic expansion for the weighted Bergman kernel related to these bundles.
Findings
Defined ampleness for line bundles on orbifolds with cyclic quotient singularities
Proved a global asymptotic expansion for the weighted Bergman kernel
Linked ampleness to embeddings in weighted projective space
Abstract
We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated to such a line bundle.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Algebra and Geometry