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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 4, Pages 159–174 (Mi izv8349)  

This article is cited in 18 scientific papers (total in 18 papers)

On $G$-Fano threefolds

Yu. G. Prokhorov

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: We study Fano threefolds with terminal Gorenstein singularities admitting a ‘minimal’ action of a finite group. We prove that under certain additional assumptions such a variety contains no planes. We also obtain upper bounds for the number of singular points of certain Fano threefolds with terminal factorial singularities.

Keywords: birational map, Fano variety, terminal singularity, divisor, linear system.

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


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English version:
Izvestiya: Mathematics, 2015, 79:4, 795–808

Bibliographic databases:

ArXiv: 1506.07873
UDC: 512.76
MSC: 14E07, 14J45, 14J30, 14J50, 14E07, 14E30
Received: 01.02.2015
Revised: 08.02.2015

Citation: Yu. G. Prokhorov, “On $G$-Fano threefolds”, Izv. RAN. Ser. Mat., 79:4 (2015), 159–174; Izv. Math., 79:4 (2015), 795–808

Citation in format AMSBIB
\by Yu.~G.~Prokhorov
\paper On $G$-Fano threefolds
\jour Izv. RAN. Ser. Mat.
\yr 2015
\vol 79
\issue 4
\pages 159--174
\jour Izv. Math.
\yr 2015
\vol 79
\issue 4
\pages 795--808

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    This publication is cited in the following articles:
    1. Yu. G. Prokhorov, “Singular Fano threefolds of genus 12”, Sb. Math., 207:7 (2016), 983–1009  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. Avilov, “Automorphisms of Singular Cubic Threefolds and the Cremona Group”, Math. Notes, 100:3 (2016), 482–485  mathnet  crossref  crossref  mathscinet  isi  elib
    3. 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
    4. Yuri G. Prokhorov, “$\mathbb Q$-Fano threefolds of index $7$”, Proc. Steklov Inst. Math., 294 (2016), 139–153  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. E. Yasinsky, “Subgroups of odd order in the real plane Cremona group”, Journal of Algebra, 461 (2016), 87–120  mathnet  crossref  mathscinet  zmath  isi  scopus
    6. Yu. G. Prokhorov, “On the Number of Singular Points of Terminal Factorial Fano Threefolds”, Math. Notes, 101:6 (2017), 1068–1073  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Vik. S. Kulikov, E. I. Shustin, “On $G$-Rigid Surfaces”, Proc. Steklov Inst. Math., 298 (2017), 133–151  mathnet  crossref  crossref  isi  elib
    8. Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509  mathnet  mathscinet
    9. E. A. Yasinsky, “$p$-Subgroups in automorphism groups of real del Pezzo surfaces”, Dokl. Math., 97:2 (2018), 129–130  mathnet  crossref  crossref  zmath  isi  elib  scopus
    10. 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
    11. I. Krylov, “Birational geometry of del Pezzo fibrations with terminal quotient singularities”, J. Lond. Math. Soc.-Second Ser., 97:2 (2018), 222–246  crossref  mathscinet  zmath  isi  scopus
    12. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
    13. A. G. Kuznetsov, “On linear sections of the spinor tenfold. I”, Izv. Math., 82:4 (2018), 694–751  mathnet  crossref  crossref  adsnasa  isi  elib
    14. A. Avilov, “Automorphisms of singular three-dimensional cubic hypersurfaces”, Eur. J. Math., 4:3, 2, SI (2018), 761–777  crossref  mathscinet  isi  scopus
    15. Yu. Prokhorov, M. Zaidenberg, “Fano–Mukai fourfolds of genus 10 as compactifications of $\mathbb{C}^4$”, Eur. J. Math., 4:3, 2, SI (2018), 1197–1263  crossref  mathscinet  isi  scopus
    16. V. L. Popov, “Compressible finite groups of birational automorphisms”, Dokl. Math., 98:2 (2018), 413–415  mathnet  crossref  zmath  isi  scopus
    17. Yu. Prokhorov, C. Shramov, “$p$-subgroups in the space Cremona group”, Math. Nachr., 291:8-9 (2018), 1374–1389  crossref  mathscinet  zmath  isi  scopus
    18. Yu. Prokhorov, C. Shramov, “Finite groups of birational selfmaps of threefolds”, Math. Res. Lett., 25:3 (2018), 957–972  crossref  mathscinet  zmath  isi
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