Abstract
Understanding the complement of the co\-amoeba 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.
Citation
Mikael Passare. Frank Sottile. "Discriminant coamoebas through homology." J. Commut. Algebra 5 (3) 413 - 440, FALL 2013. https://doi.org/10.1216/JCA-2013-5-3-413
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