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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 5, Pages 3–36 (Mi izv586)  

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

The topological classification of Fano surfaces of real three-dimensional cubics

V. A. Krasnov

P. G. Demidov Yaroslavl State University

Abstract: We consider surfaces whose points are the lines on the real three-dimensional varieties of degree 3. These surfaces are called Fano surfaces. This paper deals with finding the topological types, that is, a topological classification, of real Fano surfaces. Moreover, we prove that the equivariant topological type of the corresponding complex Fano surface with the involution of complex conjugation determines the rigid isotopy class of the corresponding real three-dimensional cubic.

DOI: https://doi.org/10.4213/im586

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English version:
Izvestiya: Mathematics, 2007, 71:5, 863–894

Bibliographic databases:

UDC: 512.7
MSC: 14PXX, 14P25
Received: 07.06.2005

Citation: V. A. Krasnov, “The topological classification of Fano surfaces of real three-dimensional cubics”, Izv. RAN. Ser. Mat., 71:5 (2007), 3–36; Izv. Math., 71:5 (2007), 863–894

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. Finashin S., Kharlamov V., “Deformation classes of real four-dimensional cubic hypersurfaces”, J. Algebraic Geom., 17:4 (2008), 677–707  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. A. Krasnov, “The Albanese Map of the Fano Surface of a Real $M$-Cubic Threefold”, Math. Notes, 84:3 (2008), 356–362  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. V. A. Krasnov, “Topological Classification of Real Three-Dimensional Cubics”, Math. Notes, 85:6 (2009), 841–847  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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