Abstract For a system of polynomial equations, whose coefficients depend on parameters, the Newton polyhedron of its discriminant is
computed in terms of the Newton polyhedra of the coefficients. This leads to an explicit formula (involving Euler obstructions
of toric varieties) in the unmixed case, suggests certain open questions in general, and generalizes a number of similar known
results (Gelfand et al. in Discriminants, resultants, and multidimensional determinants. Birkhäuser, Boston, 1994; Sturmfels in J. Algebraic Comb. 32(2):207–236, 1994; McDonald in Discrete Comput. Geom. 27:501–529, 2002; Gonzalez-Perez in Can. J. Math. 52(2):348-368, 2000; Esterov and Khovanskii in Funct. Anal. Math. 2(1), 2008).
computed in terms of the Newton polyhedra of the coefficients. This leads to an explicit formula (involving Euler obstructions
of toric varieties) in the unmixed case, suggests certain open questions in general, and generalizes a number of similar known
results (Gelfand et al. in Discriminants, resultants, and multidimensional determinants. Birkhäuser, Boston, 1994; Sturmfels in J. Algebraic Comb. 32(2):207–236, 1994; McDonald in Discrete Comput. Geom. 27:501–529, 2002; Gonzalez-Perez in Can. J. Math. 52(2):348-368, 2000; Esterov and Khovanskii in Funct. Anal. Math. 2(1), 2008).
- Content Type Journal Article
- DOI 10.1007/s00454-010-9242-7
- Authors
- A. Esterov, Universite de Nice—Sophia Antipolis Parc Valrose Laboratoire J.-A. Dieudonne 06108 Nice Cedex 02 France
- Journal Discrete and Computational Geometry
- Online ISSN 1432-0444
- Print ISSN 0179-5376
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