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

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。

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

The base space of the universal unfolding of isolated hypersurface singularities can be equipped 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  and  on the pull back bundles of the complex tangent bundle H:=π*T^(1,0)_M, where π:?times;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 isomorphism is given.