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Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface (1811.00992v2)
Published 2 Nov 2018 in math.DG, math.CV, and math.SP
Abstract: We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive 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.