Arrangements and Frobenius like structures

Alexander Varchenko

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arXiv · 1210.3802

Arrangements and Frobenius like structures

Alexander Varchenko

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Abstract

We consider a family of generic weighted arrangements of $n$ hyperplanes in $\C^k$ and show that the Gauss-Manin connection for the associated hypergeometric integrals, the contravariant form on the space of singular vectors, and the algebra of functions on the critical set of the master function define a Frobenius like structure on the base of the family. As a result of this construction we show that the matrix elements of the linear operators of the Gauss-Manin connection are given by the 2k+1-st derivatives of a single function on the base of the family, the function called the potential of second kind, see formula (6.46).

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Alexander Varchenko. 2014-09-19. Arrangements and Frobenius like structures. https://arxiv.org/abs/1210.3802

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