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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 5, Pages 1062–1081 (Mi izv1660)  

This article is cited in 6 scientific papers (total in 6 papers)

Singularities of the theta divisor of the intermediate Jacobian of a double cover of $P^3$ of index two

A. S. Tikhomirov


Abstract: In this paper a theorem is proved on the singularities of the Poincaré theta divisor $\Theta$ of the intermediate Jacobian of a body $X$, a double cover of $P^3$ of index two: the codimension of $\Theta$ in $J_3(X)$ is two. Hence a) $X$ is not rational, b) $(J_3(X),\Theta)$ is not a Prym variety, and, as a consequence, c) $X$ has no structure of a bundle of conics.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 21:2, 355–373

Bibliographic databases:

UDC: 513.6
MSC: 14K30
Received: 19.01.1982

Citation: A. S. Tikhomirov, “Singularities of the theta divisor of the intermediate Jacobian of a double cover of $P^3$ of index two”, Izv. Akad. Nauk SSSR Ser. Mat., 46:5 (1982), 1062–1081; Math. USSR-Izv., 21:2 (1983), 355–373

Citation in format AMSBIB
\Bibitem{Tik82}
\by A.~S.~Tikhomirov
\paper Singularities of the theta divisor of the intermediate Jacobian of a~double cover of~$P^3$ of index two
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 5
\pages 1062--1081
\mathnet{http://mi.mathnet.ru/izv1660}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=675531}
\zmath{https://zbmath.org/?q=an:0534.14024}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 2
\pages 355--373
\crossref{https://doi.org/10.1070/IM1983v021n02ABEH001795}


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    Erratum

    This publication is cited in the following articles:
    1. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. 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
    3. A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150  mathnet  crossref  crossref  isi  elib
    6. Cheltsov I. Przyjalkowski V. Shramov C., “Which Quartic Double Solids Are Rational?”, J. Algebr. Geom., 28:2 (2019), 201–243  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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