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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 4, Pages 19–68 (Mi izv894)  

This article is cited in 3 scientific papers (total in 3 papers)

Multiplicative intersection theory and complex tropical varieties

B. Ya. Kazarnovskii

Scientific Technical Centre "Informregistr"

Abstract: We develop an intersection theory for subvarieties of a torus. Besides the number of intersection points for a generic pair of subvarieties of complementary dimensions, this theory takes into account the product of these points as elements of the ambient torus. In the case of a complete intersection of divisors, our intersection theory yields Bernshtein's formula for the number of roots of a system as well as Khovanskii's formula for their product. When constructing this theory, we naturally encounter ‘piecewise-linear’ subsets of the torus which are referred to as complex tropical varieties.

DOI: https://doi.org/10.4213/im894

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English version:
Izvestiya: Mathematics, 2007, 71:4, 673–720

Bibliographic databases:

UDC: 512.7+514.172
MSC: 14M25, 52B20
Received: 05.08.2004
Revised: 05.10.2006

Citation: B. Ya. Kazarnovskii, “Multiplicative intersection theory and complex tropical varieties”, Izv. RAN. Ser. Mat., 71:4 (2007), 19–68; Izv. Math., 71:4 (2007), 673–720

Citation in format AMSBIB
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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. Yang J.J., “Tropical Severi Varieties”, Port Math., 70:1 (2013), 59–91  crossref  mathscinet  zmath  isi  elib  scopus
    2. B. Ya. Kazarnovskii, “On the Action of the Complex Monge–Ampère Operator on Piecewise Linear Functions”, Funct. Anal. Appl., 48:1 (2014), 15–23  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. B. Ya. Kazarnovskii, “Action of the complex Monge–Ampère operator on piecewise-linear functions and exponential tropical varieties”, Izv. Math., 78:5 (2014), 902–921  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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