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FALL 2013 Discriminant coamoebas through homology
Mikael Passare, Frank Sottile
J. Commut. Algebra 5(3): 413-440 (FALL 2013). DOI: 10.1216/JCA-2013-5-3-413


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.


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Mikael Passare. Frank Sottile. "Discriminant coamoebas through homology." J. Commut. Algebra 5 (3) 413 - 440, FALL 2013.


Published: FALL 2013
First available in Project Euclid: 13 January 2014

zbMATH: 1312.14086
MathSciNet: MR3161741
Digital Object Identifier: 10.1216/JCA-2013-5-3-413

Primary: 14H45 , 14T05

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

Vol.5 • No. 3 • FALL 2013
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