Discriminant coamoebas through homology
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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. 2013 Rocky Mountain Mathematics Consortium.
Journal of Commutative Algebra
author list (cited authors)
Passare, M., & Sottile, F.
complete list of authors
Passare, Mikael||Sottile, Frank