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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 5, Pages 1121–1197 (Mi izv1601)  

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

The Fano surface of the Veronese double cone

A. S. Tikhomirov


Abstract: This article studies the Fano surface $\mathscr F$ of lines on the Veronese double cone $X$ branched in its intersection with a cubic in $P^6$; it is the last variety in the series of Fano 3-folds of index two. The irregularity of the surface $\mathscr F$ is computed, its Abel–Jacobi mapping $\Phi$ into the intermediate Jacobian of the body $X$ is constructed, the Gauss mapping for $\Phi(\mathscr F)$ is studied, and a theorem on uniquely recovering $X$ from $\Phi(\mathscr F)$ is proved.
Bibliography: 22 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:2, 377–443

Bibliographic databases:

UDC: 513.6
MSC: 14J25
Received: 07.04.1981

Citation: A. S. Tikhomirov, “The Fano surface of the Veronese double cone”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981), 1121–1197; Math. USSR-Izv., 19:2 (1982), 377–443

Citation in format AMSBIB
\Bibitem{Tik81}
\by A.~S.~Tikhomirov
\paper The Fano surface of the Veronese double cone
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 5
\pages 1121--1197
\mathnet{http://mi.mathnet.ru/izv1601}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=637619}
\zmath{https://zbmath.org/?q=an:0501.14024|0492.14030}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 2
\pages 377--443
\crossref{https://doi.org/10.1070/IM1982v019n02ABEH001423}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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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