Toric Residues
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 October 1994
 arXiv:
 arXiv:alggeom/9410017
 Bibcode:
 1994alg.geom.10017C
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 21 pages, TeX (C Version 3.14t3)