Elimination Theory in Codimension 2
نویسندگان
چکیده
Sparse elimination theory concerns the study of Chow forms and discriminants associated with toric varieties, that is, subvarieties of projective space which are parametrized by monomials (Sturmfels, 1993; Gel’fand et al., 1994). This theory has its origin in the work of Gel’fand et al. on multivariate hypergeometric functions (Gel’fand et al., 1989). The singularities of these functions occur on the projectively dual hypersurfaces to the torus orbit closures on the given toric variety X. The singular locus of the hypergeometric system is described by the full discriminant of X, which is a natural specialization of the Chow form. Classical hypergeometric functions in one variable arise when X is a toric hypersurface, defined by one homogeneous binomial equation x1 1 · · ·xr r = x br+1 r+1 · · ·xn n . The Chow form of this hypersurface X is just its defining polynomial. The discriminant of X equals, up to an integer factor (Gel’fand et al., 1994, Section 9.1),
منابع مشابه
2 7 Fe b 20 01 Elimination Theory in Codimension Two
New formulas are given for Chow forms, discriminants and resultants arising from (not necessarily normal) toric varieties of codimension 2. The Newton polygon of the discriminant is determined exactly.
متن کاملElimination Theory in Codimension Two
New formulas are given for Chow forms, discriminants and resultants arising from (not necessarily normal) toric varieties of codimension 2. The Newton polygon of the discriminant is determined exactly.
متن کاملElimination theory in codimension one and applications
In these notes, we present a general framework to compute the codimension one part of the elimination ideal of a system of homogeneous polynomials. It is based on the computation of the so-called MacRae’s invariants that we will obtain by means of determinants of complexes. Our approach mostly uses tools from commutative algebra. We begin with some basics on elimination theory and then introduc...
متن کاملComplete Intersections in Toric Ideals
We present examples which show that in dimension higher than one or codimension higher than two, there exist toric ideals IA such that no binomial ideal contained in IA and of the same dimension is a complete intersection. This result has important implications in sparse elimination theory and in the study of the Horn system of partial differential equations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Symb. Comput.
دوره 34 شماره
صفحات -
تاریخ انتشار 2002