Arrangements and Frobenius like structures
Algebraic Geometry
2014-09-22 v4 Combinatorics
Exactly Solvable and Integrable Systems
Abstract
We consider a family of generic weighted arrangements of hyperplanes in 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).
Cite
@article{arxiv.1210.3802,
title = {Arrangements and Frobenius like structures},
author = {Alexander Varchenko},
journal= {arXiv preprint arXiv:1210.3802},
year = {2014}
}
Comments
AmsLaTeX, 55 pages, misprints corrected, a references added, abstract and introduction extended