Toric Residues

Details Toric Residues Toric Residues

1994-10-19

arxiv.org/abs/alg-geom/9410017v1

Mathematics

Algebraic Geometry

21 pages, TeX (C Version 3.14t3)

Scientific paper

In ${\bf C}^{n+1}$, one can show that the residue of $n+1$ homogeneous forms of the same degree equals the integral of a certain $(n,n)$ form over ${\bf P}^n$. Furthermore, the Jacobian of the forms has nonzero residue equal to a certain intersection number. In this paper, we generalize these results to an arbitrary projective toric variety. In particular, we define a toric version of the Jacobian and show that it has the correct properties, and we give various integral formulas for the toric residue. We also review some commutative algebra results of Batyrev and Danilov and discuss the relation between the trace map and the Dolbeault isomorphism.

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