Discriminant coamoebas through homology

Mikael Passare; Frank Sottile

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arXiv · 1201.6649

Discriminant coamoebas through homology

Mikael Passare·Frank Sottile

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Abstract

Understanding the complement of the coamoeba of a (reduced) A-discriminant is one approach to studying the monodromy of solutions to the corresponding system of A-hypergeometric differential equations. Nilsson and Passare described the structure of the coamoeba and its complement (a zonotope) when the reduced A-discriminant is a function of two variables. Their main result was that the coamoeba and zonotope form a cycle which is equal to the fundamental cycle of the torus, multiplied by the normalized volume of the set A of integer vectors. That proof only worked in dimension two. Here, we use simple ideas from topology to give a new proof of this result in dimension two, one which can be generalized to all dimensions.

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BibTeX RIS

Mikael Passare, Frank Sottile. 2012-08-02. Discriminant coamoebas through homology. https://arxiv.org/abs/1201.6649

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