Szego kernels and a theorem of Tian

Details Szego kernels and a theorem of Tian Szego kernels and a theorem of Tian

2000-02-03

arxiv.org/abs/math-ph/0002009v1

Internat. Math. Res. Notices 1998, no. 6, 317--331

Physics

Mathematical Physics

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Scientific paper

We give a simple proof of Tian's theorem that the Kodaira embeddings associated to a positive line bundle over a compact complex manifold are asymptotically isometric. The proof is based on the diagonal asymptotics of the Szego kernel (i.e. the orthogonal projection onto holomorphic sections). In deriving these asymptotics we use the Boutet de Monvel-Sjostrand parametrix for the Szego kernel.

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