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Mathematics of the USSR-Sbornik, 1983, Volume 44, Issue 2, Pages 239–260
DOI: https://doi.org/10.1070/SM1983v044n02ABEH000964 (Mi sm2465) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Numerical invariants of families of lines on some Fano varieties

D. G. Markushevich
English version PDF (1291 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM1983v044n02ABEH000964
Abstract: It is known that one-dimensional families of lines lie on irrational Fano 3-folds of index 1. These families, which are the object of study in this paper, can be used to describe the birational geometry of the varieties themselves. The author computes such invariants as the genus of the parametrizing curve, the degree of the ruled surface swept out by the lines, and the number of lines lying on the variety and intersecting a given line. The theory of Chern characteristic classes and the Schubert calculus on Grassmannians are used in the computations.
Bibliography: 13 titles.
Received: 15.10.1980
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1981, Volume 116(158), Number 2(10), Pages 265–288
Bibliographic databases:
UDC: 513.66
MSC: Primary 14J30, 14D25; Secondary 14E05, 14E35
Language: English
Original paper language: Russian
Citation: D. G. Markushevich, “Numerical invariants of families of lines on some Fano varieties”, Mat. Sb. (N.S.), 116(158):2(10) (1981), 265–288; Math. USSR-Sb., 44:2 (1983), 239–260
Citation in format AMSBIB
\Bibitem{Mar81}
\by D.~G.~Markushevich
\paper Numerical invariants of families of lines on some Fano varieties
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 2(10)
\pages 265--288
\mathnet{http://mi.mathnet.ru/sm2465}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=637865}
\zmath{https://zbmath.org/?q=an:0513.14021|0492.14026}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 2
\pages 239--260
\crossref{https://doi.org/10.1070/SM1983v044n02ABEH000964}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:291
    Russian version PDF:114
    English version PDF:25
    References:38
     
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