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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.


DOI: https://doi.org/10.4213/im8349

Full text: PDF file (580 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:4, 795–808

Bibliographic databases:

ArXiv: 1506.07873
Document Type: Article
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

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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. 82, no. 4, 2018, 53–114  mathnet  crossref  crossref  adsnasa  isi  elib
    2. A. G. Kuznetsov, “On linear sections of the spinor tenfold. I”, Izv. Math., 82:4 (2018), 694–751  mathnet  crossref  crossref  adsnasa  isi  elib
    3. 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
    4. A. Avilov, “Automorphisms of Singular Cubic Threefolds and the Cremona Group”, Math. Notes, 100:3 (2016), 482–485  mathnet  crossref  crossref  mathscinet  isi  elib
    5. 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
    6. 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
    7. 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
    8. 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
    9. Vik. S. Kulikov, E. I. Shustin, “On $G$-Rigid Surfaces”, Proc. Steklov Inst. Math., 298 (2017), 133–151  mathnet  crossref  crossref  isi  elib
    10. Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509  mathnet  mathscinet
    11. 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
    12. 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
    13. 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
    14. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
    15. A. Avilov, “Automorphisms of singular three-dimensional cubic hypersurfaces”, Eur. J. Math., 4:3, 2, SI (2018), 761–777  crossref  mathscinet  isi  scopus
    16. 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
    17. V. L. Popov, “Compressible finite groups of birational automorphisms”, Dokl. Math., 98:2 (2018), 413–415  mathnet  crossref  zmath  isi  scopus
    18. Yu. Prokhorov, C. Shramov, “$p$-subgroups in the space Cremona group”, Math. Nachr., 291:8-9 (2018), 1374–1389  crossref  mathscinet  zmath  isi  scopus
    19. Yu. Prokhorov, C. Shramov, “Finite groups of birational selfmaps of threefolds”, Math. Res. Lett., 25:3 (2018), 957–972  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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