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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 2, Pages 151–176 (Mi izv4072)  

This article is cited in 1 scientific paper (total in 1 paper)

Real four-dimensional biquadrics

V. A. Krasnov

P. G. Demidov Yaroslavl State University

Abstract: We consider intersections of two real five-dimensional quadrics, which are referred to for brevity as real four-dimensional biquadrics. Their rigid isotopy classes were described long ago: there are 16 such classes. We prove that the rigid isotopy class of a non-singular real four-dimensional biquadric is uniquely determined by the topological type of its real part. To do this, we calculate the dimensions of the cohomology spaces of the real part of a four-dimensional biquadric.

Keywords: biquadrics, rigid isotopy classes, coarse isotopy classes, index function.

DOI: https://doi.org/10.4213/im4072

Full text: PDF file (607 kB)
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English version:
Izvestiya: Mathematics, 2011, 75:2, 371–394

Bibliographic databases:

UDC: 512.7
MSC: 14P25, 14N25
Received: 11.01.2009
Revised: 16.03.2009

Citation: V. A. Krasnov, “Real four-dimensional biquadrics”, Izv. RAN. Ser. Mat., 75:2 (2011), 151–176; Izv. Math., 75:2 (2011), 371–394

Citation in format AMSBIB
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\paper Real four-dimensional biquadrics
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  • http://mi.mathnet.ru/eng/izv4072
  • https://doi.org/10.4213/im4072
  • http://mi.mathnet.ru/eng/izv/v75/i2/p151

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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. V. A. Krasnov, “On intersections of two real quadrics”, Izv. Math., 82:1 (2018), 91–139  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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