Real Algebraic and Analytic Geometry |

Gale Duality for Complete Intersections.

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Submission: 2007, October 5.

*Abstract:
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 and linear forms defining the two systems also annihilate each other. 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.*

Mathematics Subject Classification (2000): 14M25, 14P25, 52C35.

Keywords and Phrases: sparse polynomial system, hyperplane arrangement, master function, fewnomial.

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