منابع مشابه
Gale Duality for Complete Intersections
We show that every complete intersection defined by Laurent polynomials in an algebraic torus is isomorphic to a complete intersection defined by master functions in the complement of a hyperplane arrangement, and vice versa. We call systems defining such isomorphic schemes Gale dual systems because the exponents of the monomials in the polynomials annihilate the weights of the master functions...
متن کامل2 6 Ju n 20 07 GALE DUALITY FOR COMPLETE INTERSECTIONS
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 al...
متن کاملGale Duality and Koszul Duality
Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories ...
متن کاملCriteria for complete intersections
We establish two criteria for certain local algebras to be complete intersections. These criteria play an important role in A. Wiles’s proof that all semi-stable elliptic curves over Q are modular. Introduction In this paper we discuss two results in commutative algebra that are used in A. Wiles’s proof that all semi-stable elliptic curves over Q are modular [11]. We first fix some notation tha...
متن کاملGale duality bounds for roots of polynomials with nonnegative coefficients
We bound the location of roots of polynomials that have nonnegative coefficients with respect to a fixed but arbitrary basis of the vector space of polynomials of degree at most d. For this, we interpret the basis polynomials as vector fields in the real plane, and at each point in the plane analyze the combinatorics of the Gale dual vector configuration. We apply our technique to bound the loc...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2008
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2372