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Tr. Mat. Inst. Steklova, 2016, Volume 294, Pages 152–166 (Mi tm3740)  

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

$\mathbb Q$-Fano threefolds of index $7$

Yuri G. Prokhorov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We show that if the inequality $\dim\mathopen|-K_X|\ge15$ holds for a $\mathbb Q$-Fano threefold $X$ of Fano index $7$, then $X$ is isomorphic to one of the following varieties: $\mathbb P(1^2,2,3)$, $X_6\subset\mathbb P(1,2^2,3,5)$, or $X_6\subset\mathbb P(1,2,3^2,4)$.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968516030092

Full text: PDF file (276 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 139–153

Bibliographic databases:

ArXiv: 1603.01706
Document Type: Article
UDC: 512.7
Received: March 16, 2016

Citation: Yuri G. Prokhorov, “$\mathbb Q$-Fano threefolds of index $7$”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 152–166; Proc. Steklov Inst. Math., 294 (2016), 139–153

Citation in format AMSBIB
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\pages 152--166
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    This publication is cited in the following articles:
    1. Victor V. Przyjalkowski, Constantin A. Shramov, “Double quadrics with large automorphism groups”, Proc. Steklov Inst. Math., 294 (2016), 154–175  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509  mathnet  mathscinet
    3. A. G. Kuznetsov, Yu. G. Prokhorov, C. A. Shramov, “Hilbert schemes of lines and conics and automorphism groups of Fano threefolds”, Jap. J. Math., 13:1 (2018), 109–185  crossref  mathscinet  zmath  isi  scopus
    4. E. A. Yasinsky, “$p$-subgroups in automorphism groups of real del Pezzo surfaces”, Dokl. Math., 97:2 (2018), 129–130  mathnet  crossref  zmath  isi  scopus
    5. Yu. G. Prokhorov, C. A. Shramov, “$p$ -subgroups in the space Cremona group”, Math. Nachr., 291:8-9 (2018), 1374–1389  crossref  mathscinet  zmath  isi  scopus
    6. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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