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

YE Xuanming; LIN Jiezhu

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

更新时间：2023-12-11

- An Constructional Proof for the Existence of the Formal Isomorphism Between Two Flat Meromorphic Connections on a Frobenius -Manifold with a tt*Structure
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 54, Issue 1, Pages: 5-9(2015)
- 作者机构：
  
  1. 中山大学数学与计算科学学院,广东,广州,510275
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2015，
  
  Published Online：25 January 2015，
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YE Xuanming, LIN Jiezhu. An Constructional Proof for the Existence of the Formal Isomorphism Between Two Flat Meromorphic Connections on a Frobenius -Manifold with a tt*Structure. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 54(1):5-9(2015)
DOI：

YE Xuanming, LIN Jiezhu. An Constructional Proof for the Existence of the Formal Isomorphism Between Two Flat Meromorphic Connections on a Frobenius -Manifold with a tt*Structure. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 54(1):5-9(2015) DOI：

摘要

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

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。

Abstract

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



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.

关键词

Frobeniu流形tt*-结构CDV-结构平坦亚纯联络Poincare秩

Keywords

Frobenius manifoldstt*structuresCDVstructuresflat meromorphic connectionsPoincare rank

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