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Mosc. Math. J., 2002, Volume 2, Number 1, Pages 99–112 (Mi mmj47)  

This article is cited in 12 scientific papers (total in 12 papers)

Toric geometry and Grothendieck residues

O. A. Gelfonda, A. G. Khovanskiibcd

a 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 $P_1=…=P_n=0$ 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.

DOI: https://doi.org/10.17323/1609-4514-2002-2-1-99-112

Full text: http://www.ams.org/.../abst2-1-2002.html
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MSC: 14M25
Received: September 19, 2001
Language:

Citation: O. A. Gelfond, A. G. Khovanskii, “Toric geometry and Grothendieck residues”, Mosc. Math. J., 2:1 (2002), 99–112

Citation in format AMSBIB
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\by O.~A.~Gelfond, A.~G.~Khovanskii
\paper Toric geometry and Grothendieck residues
\jour Mosc. Math.~J.
\yr 2002
\vol 2
\issue 1
\pages 99--112
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\crossref{https://doi.org/10.17323/1609-4514-2002-2-1-99-112}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Batyrev, E. N. Materov, “Toric residues and mirror symmetry”, Mosc. Math. J., 2:3 (2002), 435–475  mathnet  mathscinet  zmath  elib
    2. Soprounov I., “Residues and tame symbols on toroidal varieties”, Compos. Math., 140:6 (2004), 1593–1613  crossref  mathscinet  zmath  isi
    3. Khetan A., Soprounov I., “Combinatorial construction of toric residues”, Ann. Inst. Fourier (Grenoble), 55:2 (2005), 511–548  crossref  mathscinet  zmath  isi
    4. D'Andrea C., Khetan A., “Macaulay style formulas for toric residues”, Compos. Math., 141:3 (2005), 713–728  crossref  mathscinet  zmath  isi
    5. Soprounov I., “Toric residue and combinatorial degree”, Trans. Amer. Math. Soc., 357:5 (2005), 1963–1975  crossref  mathscinet  zmath  isi
    6. E. Soprunova, “Zeros of systems of exponential sums and trigonometric polynomials”, Mosc. Math. J., 6:1 (2006), 153–168  mathnet  mathscinet  zmath
    7. B. Ya. Kazarnovskii, “Multiplicative intersection theory and complex tropical varieties”, Izv. Math., 71:4 (2007), 673–720  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Soprunov I., “Global residues for sparse polynomial systems”, J. Pure Appl. Algebra, 209:2 (2007), 383–392  crossref  mathscinet  zmath  isi
    9. Soprunova E., “Exponential Gelfond-Khovanskii formula in dimension one”, Proc. Amer. Math. Soc., 136:1 (2008), 239–245  crossref  mathscinet  zmath  isi
    10. Soprunov I., “Toric Complete Intersection Codes”, J. Symbolic Comput., 50 (2013), 374–385  crossref  mathscinet  zmath  isi
    11. Weimann M., “Concavity, Abel Transform and the Abel-Inverse Theorem in Smooth Complete Toric Varieties”, Collect. Math., 64:1 (2013), 111–133  crossref  mathscinet  zmath  isi  elib
    12. A. G. Khovanskii, Leonid Monin, “The resultant of developed systems of Laurent polynomials”, Mosc. Math. J., 17:4 (2017), 717–740  mathnet
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