This article is cited in 19 papers

Toric geometry and Grothendieck residues

O. A. Gelfond^a, A. G. Khovanskii<sup>bcd

a</sup> Scientific Research Institute for System Studies of RAS
^b University of Toronto
^c Independent University of Moscow
^d Institute of Systems Analysis, Russian Academy of Sciences

Abstract: We consider a system of $n$ algebraic equations $P_1=\dots=P_n=0$ in the torus $(\mathbb C\setminus 0)^n$. It is assumed that the Newton polyhedra of the equations are in a sufficiently general position with respect to one another. Let $\omega$ be any rational $n$-form which is regular on $(\mathbb C\setminus0)^n$ outside the hypersurface $P_1\dotsb P_n=0$. Formerly we have announced an explicit formula for the sum of the Grothendieck residues of the form $\omega$ at all roots of the system of equations. In the present paper this formula is proved.

Key words and phrases: Grothendieck residues, Newton polyhedra, toric varieties.

MSC: 14M25

Received: September 19, 2001

Language: English

DOI: 10.17323/1609-4514-2002-2-1-99-112

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