Flat structure for the simple elliptic singularity of type $\widetilde {\bf E_6}$ and Jacobi form

Ikuo Satake

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arXiv · hep-th/9307009

Flat structure for the simple elliptic singularity of type $\widetilde {\bf E_6}$ and Jacobi form

Ikuo Satake

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Abstract

In order to construct the inverse mapping of the period mapping for the primitive form for the semi-universal deformation of a simple elliptic singularity, K.Saito introduced in [5] the ``flat structure'' for the extended affine root system. In section 3, we construct explicitly the flat theta invariants in the case of type $E_6$ using the Jacobi form introduced by Wirthmüller [7]. Combining the results of Kato [3], Noumi [4] (explicit description of the flat coordinates), this gives an answer to Jacobi's inversion problem (up to linear isomorphism) of this period mapping for a simple elliptic singularity of type $\tilde E_6$ (see also [6]). The details will be published elsewhere.

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Ikuo Satake. 1993-07-02. Flat structure for the simple elliptic singularity of type $\widetilde {\bf E_6}$ and Jacobi form. https://arxiv.org/abs/hep-th/9307009

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