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. 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, 2015,54(1):5-9.
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, 2015,54(1):5-9.DOI:
The base space of the universal unfolding of isolated hypersurface singularities can be equipped with a geometry structure
which was atomizated by Hertling as CVstructures.Hertling also proved that this structure is compatible with the canonical Frobenius manifold on the base space and gave CDVstructure. Given any CDVstructure M
there are two natural flat meromorphic connections and on the pullback 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 subvarieties{0
∞}×M.If M is a semisimple 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.