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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 6, Pages 1159–1174 (Mi izv1701)  

This article is cited in 10 scientific papers (total in 10 papers)

On Fano varieties of genus 6

N. P. Gushel'


Abstract: In this paper it is proved that any nonsingular Fano variety $V_{10}$ of genus $6$ in $\mathbf P^7$ with $\operatorname{Pic}V_{10}\simeq\mathbf ZK_V$ is either a section $V_{10}^3$ of the Grassmannian $G(1,4)$ of lines in $\mathbf P^4$ by two hyperplanes and a quadric under the Plücker embedding of $G(1,4)$ in $\mathbf P^9$ or is the intersection ${V_{10}^3}'$ of a quadric and a cone over a section of $G(1,4)$ by a subspace of codimension $3$.
Bibliography: 13 titles.

Full text: PDF file (1672 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1983, 21:3, 445–459

Bibliographic databases:

UDC: 513.6
MSC: 14J30
Received: 30.11.1981

Citation: N. P. Gushel', “On Fano varieties of genus 6”, Izv. Akad. Nauk SSSR Ser. Mat., 46:6 (1982), 1159–1174; Math. USSR-Izv., 21:3 (1983), 445–459

Citation in format AMSBIB
\Bibitem{Gus82}
\by N.~P.~Gushel'
\paper On Fano varieties of genus 6
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 6
\pages 1159--1174
\mathnet{http://mi.mathnet.ru/izv1701}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=682488}
\zmath{https://zbmath.org/?q=an:0554.14014}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 3
\pages 445--459
\crossref{https://doi.org/10.1070/IM1983v021n03ABEH001801}


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  • http://mi.mathnet.ru/eng/izv/v46/i6/p1159

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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. N. P. Gushel', “Fano varieties of genus 8”, Russian Math. Surveys, 38:1 (1983), 192–193  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. V. Batyrev, “On some numerical characteristics of multidimensional Fano varieties”, Math. USSR-Izv., 26:2 (1986), 423–435  mathnet  crossref  mathscinet  zmath
    3. V. A. Iskovskikh, “Double projection from a line on Fano threefolds of the first kind”, Math. USSR-Sb., 66:1 (1990), 265–284  mathnet  crossref  mathscinet  zmath  isi
    4. Atanas Iliev, “Lines on the Gushel' threefold”, Indagationes Mathematicae, 5:3 (1994), 307  crossref
    5. Priska Jahnke, Thomas Peternell, Ivo Radloff, “Threefolds with big and nef anticanonical bundles I”, Math Ann, 333:3 (2005), 569  crossref  mathscinet  zmath  isi
    6. V. V. Przyjalkowski, “Gromov–Witten invariants of Fano threefolds of genera 6 and 8”, Sb. Math., 198:3 (2007), 433–446  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Kuznetsov A. Perry A., “Derived categories of cyclic covers and their branch divisors”, Sel. Math.-New Ser., 23:1 (2017), 389–423  crossref  mathscinet  zmath  isi  scopus
    8. Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509  mathnet  mathscinet
    9. Debarre O., Kuznetsov A., “Gushel-Mukai Varieties: Classification and Birationalities”, Algebraic Geom., 5:1 (2018), 15–76  crossref  isi
    10. Kuznetsov A. Perry A., “Derived Categories of Gushel-Mukai Varieties”, Compos. Math., 154:7 (2018), 1362–1406  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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