Geometric quantization results for semi-positive line bundles on a Riemann surface

Author:

George Marinescu, Nikhil Savale

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Mathematical Physics (math-ph), Complex Variables (math.CV), Probability (math.PR)

journal:

date:

2023-10-21 16:00:00

Abstract

In earlier work the authors proved the Bergman kernel expansion for semipositive line bundles over a Riemann surface whose curvature vanishes to atmost finite order at each point. Here we explore the related results and consequences of the expansion in the semipositive case including: Tian's approximation theorem for induced Fubini-Study metrics, leading order asymptotics and composition for Toeplitz operators, asymptotics of zeroes for random sections and the asymptotics of holomorphic torsion.

PDF: Geometric quantization results for semi-positive line bundles on a Riemann surface.pdf