带tt*-结构的Frobenius流形上两个平坦亚纯联络形式同构的存在性

An Constructional Proof for the Existence of the Formal Isomorphism Between Two Flat Meromorphic Connections on a Frobenius Manifold with a tt*-Structure

超曲面奇异的半通用展开的基空间上可以自然赋予一个几何结构,Hertling把该结构公理化称之为CV-结构,并证明了该几何结构和基空间上的典范Frobenius流形是相容的,从而给出了CDV-结构。给定任意的CDV-结构M,在切丛的拉回丛H:=π*T(1,0)M上,有两个自然地平坦亚纯联络,且奇点只在{0}×M和{∞}×M上。如果该CDV-结构中的Frobenius流形结构是一个半单Frobenius流形时,这两个联络都是非正则的亚纯联络。通过已知的非正则平坦亚纯联络分类定理得到形式同构存在性定理:这两个自然的平坦亚纯联络是形式同构的。将给出该形式同构存在性定理的另一个证明:显式构造性证明。

The base space of the universal unfolding of isolated hypersurface singularities can be e-quipped with a geometry structure,which was atomizated by Hertling as CV-structures.Hertling also proved that this structure is compatible with the canonical Frobenius manifold on the base space and gave CDV-structure.Given any CDV-structure M,there are two natural flat meromorphic connections D and on the pull-back bundles of the complex tangent bundle H：π＊T（1,0）M ,where π：C^M→ M,and the singularities of these two connections are sub-varieties {0,∞}^M.If M is a semi-simple Frobenius manifold,it is known that these two meromorphic connections have irregular singularities.It is concluded that there exists a formal isomorphism between these two formalized bundles with connections by applying the classifications of irregular flat meromorphic connections.A constructional proof of the formal isomor-phism is given.