Szego Kernels and a Theorem of Tian
نویسنده
چکیده
A variety of results in complex geometry and mathematical physics depend upon the analysis of holomorphic sections of high powers L⊗N of holomorphic line bundles L → M over compact Kähler manifolds ([A][Bis][Bis.V] [Bou.1][Bou.2][B.G][D][Don] [G][G.S][K][Ji] [T] [W]). The principal tools have been Hörmander’s L-estimate on the ∂̄-operator over M [T], the asymptotics of heat kernels kN (t, x, y) for associated Laplacians [Bis][Bis.V][D][Bou.1][Bou.2][G], the method of stationary phase for formal functional integrals [A][W] and the microlocal analysis of Szegö and Bergman kernels [B.F.G][B.S][B.G]. In this note we wish to apply the latter methods, specifically the Boutet de Monvel-Sjöstrand parametrix for the Szegö kernel, to a problem in complex geometry. Our purpose is to prove the following theorem:
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