中山大学学报(自然科学版)
中山大學學報(自然科學版)
중산대학학보(자연과학판)
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS SUNYATSENI
2015年
1期
5-9
,共5页
Frobeniu 流形%tt* -结构%CDV -结构%平坦亚纯联络%Poincare 秩
Frobeniu 流形%tt* -結構%CDV -結構%平坦亞純聯絡%Poincare 秩
Frobeniu 류형%tt* -결구%CDV -결구%평탄아순련락%Poincare 질
Frobenius manifolds%tt*-structures%CDV-structures%flat meromorphic connections%Poin-care rank
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。
超麯麵奇異的半通用展開的基空間上可以自然賦予一箇幾何結構,Hertling 把該結構公理化稱之為 CV-結構,併證明瞭該幾何結構和基空間上的典範 Frobenius 流形是相容的,從而給齣瞭 CDV -結構。給定任意的CDV -結構 M,在切叢的拉迴叢 H:=π*T (1,0) M上,有兩箇自然地平坦亞純聯絡,且奇點隻在{0}×M和{∞}× M上。如果該 CDV -結構中的 Frobenius 流形結構是一箇半單 Frobenius 流形時,這兩箇聯絡都是非正則的亞純聯絡。通過已知的非正則平坦亞純聯絡分類定理得到形式同構存在性定理:這兩箇自然的平坦亞純聯絡是形式同構的。將給齣該形式同構存在性定理的另一箇證明:顯式構造性證明。
초곡면기이적반통용전개적기공간상가이자연부여일개궤하결구,Hertling 파해결구공이화칭지위 CV-결구,병증명료해궤하결구화기공간상적전범 Frobenius 류형시상용적,종이급출료 CDV -결구。급정임의적CDV -결구 M,재절총적랍회총 H:=π*T (1,0) M상,유량개자연지평탄아순련락,차기점지재{0}×M화{∞}× M상。여과해 CDV -결구중적 Frobenius 류형결구시일개반단 Frobenius 류형시,저량개련락도시비정칙적아순련락。통과이지적비정칙평탄아순련락분류정리득도형식동구존재성정리:저량개자연적평탄아순련락시형식동구적。장급출해형식동구존재성정리적령일개증명:현식구조성증명。
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.