Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Airy structures and deformations of curves in surfaces   An embedded curve in a symplectic surface $\Sigma\subset X$ defines a smooth
deformation space $\mathcal{B}$ of nearby embedded curves. A key idea of
Kontsevich and Soibelman arXiv:1701.09137 [math.AG], is to equip the symplectic
surface $X$ with a foliation in order to study the deformation space
$\mathcal{B}$. The foliation, together with a vector space $V_\Sigma$ of
meromorphic differentials on $\Sigma$, endows an embedded curve $\Sigma$ with
the structure of the initial data of topological recursion, which defines a
collection of symmetric tensors on $V_\Sigma$. Kontsevich and Soibelman define
an Airy structure on $V_\Sigma$ to be a formal quadratic Lagrangian
$\mathcal{L}\subset T^*(V_\Sigma^*)$ which leads to an alternative construction
of the tensors of topological recursion. In this paper we produce a formal
series $\theta$ on $\mathcal{B}$ of meromorphic differentials on $\Sigma$ which
takes it values in $\mathcal{L}$, and use this to produce the Donagi-Markman
cubic from a natural cubic tensor on $V_\Sigma$, giving a generalisation of a
result of Baraglia and Huang, arXiv:1707.04975 [math.DG].

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org