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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 3, Pages 119–132 (Mi izv244)  

This article is cited in 10 scientific papers (total in 10 papers)

Truncation of systems of polynomial equations, ideals and varieties

B. Ya. Kazarnovskii

Scientific Technical Centre "Informregistr"

Abstract: The main result of this paper is the construction of special so-called locked polynomial ideals to represent systems of equations, and to enable the behaviour of the corresponding algebraic varieties at infinity to be controlled. A consequence of this result is the existence, modulo the action of tori, of a standard minimal toric compactification of an irreducible two-dimensional variety.

DOI: https://doi.org/10.4213/im244

Full text: PDF file (1422 kB)
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English version:
Izvestiya: Mathematics, 1999, 63:3, 535–547

Bibliographic databases:

MSC: Primary 14M25; Secondary 13F20
Received: 13.10.1997

Citation: B. Ya. Kazarnovskii, “Truncation of systems of polynomial equations, ideals and varieties”, Izv. RAN. Ser. Mat., 63:3 (1999), 119–132; Izv. Math., 63:3 (1999), 535–547

Citation in format AMSBIB
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\pages 119--132
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\pages 535--547
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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. B. Ya. Kazarnovskii, “Letter to the editors”, Izv. Math., 64:1 (2000), 221–221  mathnet  crossref  crossref  mathscinet  isi
    2. B. Ya. Kazarnovskii, “c-fans and Newton polyhedra of algebraic varieties”, Izv. Math., 67:3 (2003), 439–460  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. B. Ya. Kazarnovskii, “Multiplicative intersection theory and complex tropical varieties”, Izv. Math., 71:4 (2007), 673–720  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Proc. Steklov Inst. Math., 259 (2007), 16–34  mathnet  crossref  mathscinet  zmath  elib
    5. A. Esterov, A. Khovanskii, “Elimination theory and Newton polytopes”, Funct Anal Other Math, 2008  crossref  mathscinet  zmath
    6. Verschelde J., “Polyhedral Methods in Numerical Algebraic Geometry”, Interactions of Classical and Numerical Algebraic Geometry, Contemporary Mathematics, 496, 2009, 243–263  crossref  mathscinet  zmath  isi
    7. Danko Adrovic, Jan Verschelde, “Tropical algebraic geometry in Maple: A preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients”, Journal of Symbolic Computation, 46:7 (2011), 755  crossref  mathscinet  zmath  isi  scopus
    8. Yang J.J., “Tropical Severi Varieties”, Port Math., 70:1 (2013), 59–91  crossref  mathscinet  zmath  isi  elib  scopus
    9. B. Ya. Kazarnovskiǐ, A. G. Hovanskiǐ, “The tropical Noetherity and Gröbner bases”, St. Petersburg Math. J., 26:5 (2015), 797–811  mathnet  crossref  mathscinet  isi  elib  elib
    10. Esterov A., “Characteristic Classes of Affine Varieties and Plucker Formulas For Affine Morphisms”, J. Eur. Math. Soc., 20:1 (2018), 15–59  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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