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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 2, Pages 415–442 (Mi izv1672)  

This article is cited in 9 scientific papers (total in 9 papers)

The geometry of the Fano surface of the double cover of $P^3$ branched in a quartic

A. S. Tikhomirov


Abstract: This paper gives a computation of the irregularity of the Fano surface $\mathscr F$ of lines on the double cover $X\to P^3$ branched in a quartic. A tangent bundle theorem is proved for $\mathscr F$, from which it follows that $\mathscr F$ determines $X$ uniquely. It is shown that the Abel–Jacobi map $a\colon\operatorname{Alb}(\mathscr F)\to J_3(X)$ is an isogeny.
Bibliography: 7 titles.

Full text: PDF file (2158 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:2, 373–397

Bibliographic databases:

UDC: 512.776
MSC: 14J30
Received: 07.09.1979

Citation: A. S. Tikhomirov, “The geometry of the Fano surface of the double cover of $P^3$ branched in a quartic”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980), 415–442; Math. USSR-Izv., 16:2 (1981), 373–397

Citation in format AMSBIB
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\by A.~S.~Tikhomirov
\paper The geometry of the Fano surface of the double cover of $P^3$ branched in a~quartic
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 2
\pages 415--442
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=571103}
\zmath{https://zbmath.org/?q=an:0462.14014|0434.14023}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 2
\pages 373--397
\crossref{https://doi.org/10.1070/IM1981v016n02ABEH001313}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MK40900007}


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  • http://mi.mathnet.ru/eng/izv/v44/i2/p415

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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. A. S. Tikhomirov, “The intermediate Jacobian of the double covering of $P^3$ branched at a quartic”, Math. USSR-Izv., 17:3 (1981), 523–566  mathnet  crossref  mathscinet  zmath  isi
    2. A. S. Tikhomirov, “The Fano surface of the Veronese double cone”, Math. USSR-Izv., 19:2 (1982), 377–443  mathnet  crossref  mathscinet  zmath
    3. A. S. Tikhomirov, “Singularities of the theta divisor of the intermediate Jacobian of a double cover of $P^3$ of index two”, Math. USSR-Izv., 21:2 (1983), 355–373  mathnet  crossref  mathscinet  zmath
    4. Markushevich D.G., Tikhomirov A.S., “A parametrization of the theta divisor of the quartic double solid”, International Mathematics Research Notices, 2003, no. 51, 2747–2778  isi  elib
    5. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. L. GRUSON, F. LAYTIMI, D. S. NAGARAJ, “ON PRIME FANO THREEFOLDS OF GENUS 9”, Int. J. Math, 17:03 (2006), 253  crossref
    8. Jun-Muk Hwang, Hosung Kim, “Varieties of minimal rational tangents on double covers of projective space”, Math. Z, 2012  crossref
    9. Logachev D., “Fano Threefolds of Genus 6”, Asian J. Math., 16:3 (2012), 515–559  mathscinet  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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