Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A neighbourhood theorem for submanifolds in generalized complex geometry   We study neighbourhoods of submanifolds in generalized complex geometry. Our
first main result provides sufficient criteria for such a submanifold to admit
a neighbourhood on which the generalized complex structure is B-field
equivalent to a holomorphic Poisson structure. This is intimately tied with our
second main result, which is a rigidity theorem for generalized complex
deformations of holomorphic Poisson structures. Specifically, on a compact
manifold with boundary we provide explicit conditions under which any
generalized complex perturbation of a holomorphic Poisson structure is B-field
equivalent to another holomorphic Poisson structure. The proofs of these
results require two analytical tools: Hodge decompositions on almost complex
manifolds with boundary, and the Nash-Moser algorithm. As a concrete
application of these results, we show that on a four-dimensional generalized
complex submanifold which is generically symplectic, a neighbourhood of the
entire complex locus is B-field equivalent to a holomorphic Poisson structure.
Furthermore, we use the neighbourhood theorem to develop the theory of blowing
down submanifolds in generalized complex geometry.

30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol