Analyticity of the total ancestor potential in singularity theory
Analyticity of the total ancestor potential in singularity theory
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DOI：
10.1016/j.aim.2014.01.009
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发表时间：
2013-03
期刊：
影响因子：
--
通讯作者：
T. Milanov
中科院分区：
文献类型：
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作者：
T. Milanov
K. Saito 的本原形式理论给出了孤立奇点微变形空间上的自然半单弗罗贝尼乌斯流形结构。另一方面，吉文塔尔为弗罗贝尼乌斯流形的每个半单点引入了总祖先势的概念，并推测在奇点理论的背景下，他的定义也可以分析扩展到非半单点。在本文中，我们利用 Eynard-Orantin 递归证明了 Givental 的猜想。
K. Saito's theory of primitive forms gives a natural semi-simple Frobenius manifold structure on the space of miniversal deformations of an isolated singularity. On the other hand, Givental introduced the notion of a total ancestor potential for every semi-simple point of a Frobenius manifold and conjectured that in the settings of singularity theory his definition extends analytically to non-semisimple points as well. In this paper we prove Givental's conjecture by using the Eynard–Orantin recursion.