论文标题
表面上的通风结构和曲线的变形
Airy structures and deformations of curves in surfaces
论文作者
论文摘要
在符号表面$σ\子集x $中的嵌入式曲线定义了附近嵌入式曲线的平滑变形空间$ \ MATHCAL {B} $。 Kontsevich和Soibelman Arxiv的一个关键思想：1701.09137 [Math.ag]，是为了研究变形空间$ \ MATHCAL {B} $。叶面与$σ$上的meromorphic差异的矢量空间$v_σ$一起，将嵌入式曲线$σ$与拓扑递归的初始数据结构结构一起定义，该结构定义了$v_σ$上的对称张量的集合。 Kontsevich和Soibelman在$v_σ$上定义了一个通风的结构，使其成为正式的二次拉格朗日$ \ MATHCAL {l} \ subset t^*（v_σ^*）$，从而导致拓扑递归量的替代构造。在本文中，我们在$ = $σ$上的$ \ Mathcal {b} $上生产正式的系列$θ$上的$σ$上的差异差异，将其估价为$ \ nathcal {l} $，并用它来生产Donagi-Markman Cubic从$v_σ$上的天然立方张量产生$v_σ$的自然tensor，从而使baragia of Baragia of Baragilia和Huangia的总体化。 [Math.dg]。
An embedded curve in a symplectic surface $Σ\subset X$ 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 $V_Σ$ of meromorphic differentials on $Σ$, endows an embedded curve $Σ$ with the structure of the initial data of topological recursion, which defines a collection of symmetric tensors on $V_Σ$. Kontsevich and Soibelman define an Airy structure on $V_Σ$ to be a formal quadratic Lagrangian $\mathcal{L}\subset T^*(V_Σ^*)$ which leads to an alternative construction of the tensors of topological recursion. In this paper we produce a formal series $θ$ on $\mathcal{B}$ of meromorphic differentials on $Σ$ which takes it values in $\mathcal{L}$, and use this to produce the Donagi-Markman cubic from a natural cubic tensor on $V_Σ$, giving a generalisation of a result of Baraglia and Huang, arXiv:1707.04975 [math.DG].
