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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 378, Pages 133–170 (Mi znsl3832)  
This article is cited in 3 scientific papers (total in 3 papers)

Polynomial-time algorithms for a new model of representation of algebraic varieties (in characteristic zero)

A. L. Chistov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (780 kB) Citations (3)
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Abstract: We suggest a model of representation of algebraic varieties based on representative systems of points of their irreducible components. Deterministic polynomial-time algorithms that substantiate this model are described in characteristic zero. The main result here is a construction of the intersection of algebraic varieties. As applications, we obtain efficient algorithms for constructing the smooth stratification and smooth cover of an algebraic variety suggested by the author earlier. Bibl. 16 titles.
Key words and phrases: algebraic varieties, efficient algorithms, smooth stratification, intersection numbers.
Received: 09.09.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 174, Issue 1, Pages 71–89
DOI: https://doi.org/10.1007/s10958-011-0282-1
Bibliographic databases:
Document Type: Article
UDC: 518.5+513.6
Language: Russian
Citation: A. L. Chistov, “Polynomial-time algorithms for a new model of representation of algebraic varieties (in characteristic zero)”, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Zap. Nauchn. Sem. POMI, 378, POMI, St. Petersburg, 2010, 133–170; J. Math. Sci. (N. Y.), 174:1 (2011), 71–89
Citation in format AMSBIB
\Bibitem{Chi10}
\by A.~L.~Chistov
\paper Polynomial-time algorithms for a~new model of representation of algebraic varieties (in characteristic zero)
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 378
\pages 133--170
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3832}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 174
\issue 1
\pages 71--89
\crossref{https://doi.org/10.1007/s10958-011-0282-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952817447}
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  • https://www.mathnet.ru/eng/znsl/v378/p133
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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