Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramadanov conjecture and line bundles over compact Hermitian symmetric
  spaces   We compute the Szeg\"o kernels of the unit circle bundles of homogeneous
negative line bundles over a compact Hermitian symmetric space. We prove that
their logarithmic terms vanish in all cases and, further, that the circle
bundles are not diffeomorphic to the unit sphere in $\CC^n$ for Grassmannian
manifolds of higher ranks. In particular they provide an infinite family of
smoothly bounded strictly pseudo-convex domains on complex manifolds for which
the log terms in the Fefferman expansion of the Szeg\"o kernel vanish and which
are not diffeomorphic to the sphere. The analogous results for the Bergman
kernel are also obtained.

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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph