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 Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 1, Pages 281–304 (Mi izv8307)

Newton polytopes and irreducible components of complete intersections

A. G. Khovanskiiab

a Independent University of Moscow
b Department of Mathematics, University of Toronto

Abstract: We calculate the number of irreducible components of varieties in $(\mathbb C^*)^n$ determined by generic systems of equations with given Newton polytopes. Every such component can in its turn be given by a generic system of equations whose Newton polytopes are found explicitly. It is known that many discrete invariants of a variety can be found in terms of the Newton polytopes. Our results enable one to calculate such invariants for each irreducible component of the variety.

Keywords: Newton polytopes, mixed volume, irreducible components, holomorphic forms.

 Funding Agency Grant Number Agence Nationale de la Recherche ANR-08-BLAN-0317-01ANR-13-IS01-0001-01 This paper was written with the support of the grants ANR-08-BLAN-0317-01 and ANR-13-IS01-0001-01 of the National Research Agency.

DOI: https://doi.org/10.4213/im8307

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English version:
Izvestiya: Mathematics, 2016, 80:1, 263–284

Bibliographic databases:

UDC: 515.165.4
MSC: 14M25, 13P15, 52A39, 52B20, 32Q55
Revised: 25.02.2015

Citation: A. G. Khovanskii, “Newton polytopes and irreducible components of complete intersections”, Izv. RAN. Ser. Mat., 80:1 (2016), 281–304; Izv. Math., 80:1 (2016), 263–284

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/izv8307
• https://doi.org/10.4213/im8307
• http://mi.mathnet.ru/eng/izv/v80/i1/p281

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. K. Kaveh, A. Khovanskii, “Complete intersections in spherical varieties”, Selecta Mathematica-New Series, 22:4 (2016), 2099–2141
2. A. A. Martynyuk, “Comparison principle based on Minkowski mixed volumes for a family of differential equations”, Differ. Equ., 53:12 (2017), 1549–1556
3. Esterov A., “Galois Theory For General Systems of Polynomial Equations”, Compos. Math., 155:2 (2019), 229–245
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