Exact matrix formula for the unmixed resultant in three variables

Details Exact matrix formula for the unmixed resultant in three variables Exact matrix formula for the unmixed resultant in three variables

2003-10-30

arxiv.org/abs/math/0310478v4

Journal of Pure and Applied Algebra 198(2005) 237-256

Mathematics

Algebraic Geometry

24 pages, 2 figures, Cohomology vanishing theorem generalized with new combinatorial proof. Can state some cases of exact resu

Scientific paper

We give the first exact determinantal formula for the resultant of an unmixed sparse system of four Laurent polynomials in three variables with arbitrary support. This follows earlier work by the author on exact formulas for bivariate systems and also uses the exterior algebra techniques of Eisenbud and Schreyer. Along the way we will prove an interesting new vanishing theorem for the sheaf cohomology of divisors on toric varieties. This will allow us to describe some supports in four or more variables for which determinantal formulas for the resultant exist.

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