Bochner Laplacian and Bergman kernel expansion of semipositive line bundles on a Riemann surface

Abstract

AbstractWe generalize the results of Montgomery (Commun Math Phys 168:651–675, 1995) for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion for semipositive line bundles whose curvature vanishes at finite order. The proof exploits the relation of the Bochner Laplacian on tensor powers with the sub-Riemannian (sR) Laplacian.