Gale duality for complete intersections

Details Gale duality for complete intersections Gale duality for complete intersections

2007-06-26

arxiv.org/abs/0706.3745v4

Mathematics

Algebraic Geometry

11 pages, 3 figures

Scientific paper

We show that every complete intersection of Laurent polynomials in an algebraic torus is isomorphic to a complete intersection of master functions in the complement of a hyperplane arrangement, and vice versa. We call this association Gale duality because the exponents of the monomials in the polynomials annihilate the weights of the master functions. We use Gale duality to give a Kouchnirenko theorem for the number of solutions to a system of master functions and to compute some topological invariants of generic master function complete intersections.

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