Newton polyhedra of discriminants of projections

Details Newton polyhedra of discriminants of projections Newton polyhedra of discriminants of projections

2008-10-28

arxiv.org/abs/0810.4996v3

Discrete Comput. Geom., 44 (2010), no. 1, 96-148; Appendix: Moscow Mathematical Journal, 8 (2008), no. 3, 433-442

Mathematics

Algebraic Geometry

Revised and expanded exposition, misprints corrected, references added

Scientific paper

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 mixed fiber polyhedra and Euler obstructions of toric varieties) in the unmixed case, suggests certain open questions in general, and generalizes a number of similar known results. The argument is based on a formula for the support function of a mixed fiber body, which also suggests a new proof for existence of mixed fiber bodies.

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