Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost holomorphic embeddings in Grassmannians with applications to
  singular simplectic submanifolds   We use Donaldson's approximately holomorphic techniques to build embeddings
of a closed symplectic manifold with symplectic form of integer class in the
grassmannians Gr(r,N). We assure that these embeddings are asymptotically
holomorphic in a precise sense. We study first the particular case of
embeddings in the projective space $CP^N$ obtaining control on N. The main
reason of our study is the construction of singular determinantal submanifolds
as the intersection of the embedding with certain ``generalized Schur cycles''
defined on a product of grassmannians. It is shown that the symplectic type of
these submanifolds is quite more general that the ones obtained by Auroux as
zero sets of approximately holomorphic sections of ``very ample'' vector
bundles.

27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex