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POTENTIALS OF A FROBENIUS-LIKE STRUCTURE

Part of: Designs and configurations Basic linear algebra Singularities Symplectic geometry, contact geometry

Published online by Cambridge University Press:  28 January 2018

CLAUS HERTLING  and
ALEXANDER VARCHENKO
CLAUS HERTLING
Affiliation:
Lehrstuhl für Mathematik VI, Universität MannheimA5,6, 68131Mannheim, Germany e-mail: hertling@math.uni-mannheim.de
ALEXANDER VARCHENKO
Affiliation:
Department of Mathematics, University of North Carolina at Chapel HillChapel Hill, NC 27599-3250, USA e-mail: anv@email.unc.edu
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Abstract

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This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame, which encompasses families of arrangements. The frame uses the notion of matroids. For the proof of the existence of the potentials, a power series ansatz is made. The proof that it works requires that certain decompositions of tuples of coordinate vector fields are related by certain elementary transformations. This is shown with a nontrivial result on matroid partition.

MSC classification

Primary: 05B35: Matroids, geometric lattices
Secondary: 15A03: Vector spaces, linear dependence, rank 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 32S22: Relations with arrangements of hyperplanes
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018 , pp. 681 - 693
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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