Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of almost holomorphic sections on symplectic manifolds   We study the asymptotics of almost holomorphic sections $s \in H^0_J(M,
\omega)$ of an ample line bundle $L \to M$ over an almost complex symplectic
manifold in the sense of Boutet de Monvel-Guillemin. Such sections are defined
as the kernel of a complex which is analogous to the $\bar{\partial}$ complex
for a positive line bundle over a complex manifold. Our main result is the
scaling limit asymptotics of the Szego projectors $\Pi_N$ of powers $L^N$. The
Kodaira embedding theorem and Tian almost isometry theorem are almost immediate
consequences of the scaling limit. We also relate such almost holomorphic
sections to the asymptotically holomorphic sections in the sense of Donaldson
and Auroux.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin