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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.
Received: 05.08.2004 Revised: 05.10.2006
Citation:
B. Ya. Kazarnovskii, “Multiplicative intersection theory and complex tropical varieties”, Izv. Math., 71:4 (2007), 673–720
Linking options:
https://www.mathnet.ru/eng/im894https://doi.org/10.1070/IM2007v071n04ABEH002372 https://www.mathnet.ru/eng/im/v71/i4/p19
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Abstract page: | 537 | Russian version PDF: | 280 | English version PDF: | 18 | References: | 55 | First page: | 11 |
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