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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 3, Pages 5–22 (Mi izv433)  

This article is cited in 11 scientific papers (total in 11 papers)

On a double cone over a Veronese surface

M. M. Grinenko

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study the birational geometry of a Fano threefold that is a double covering of a cone over a Veronese surface with ramification at a non-singular section by a cubic. In particular, we consider the set of Mori structures and possible types of maximal singularities of linear systems.

DOI: https://doi.org/10.4213/im433

Full text: PDF file (1328 kB)
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English version:
Izvestiya: Mathematics, 2003, 67:3, 421–438

Bibliographic databases:

UDC: 512.6
MSC: 14E05, 14E07, 14E15, 14J30, 14J45, 14J50
Received: 21.01.2003

Citation: M. M. Grinenko, “On a double cone over a Veronese surface”, Izv. RAN. Ser. Mat., 67:3 (2003), 5–22; Izv. Math., 67:3 (2003), 421–438

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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. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. M. M. Grinenko, “Mori Structures on a Fano Threefold of Index 2 and Degree 1”, Proc. Steklov Inst. Math., 246 (2004), 103–128  mathnet  mathscinet  zmath
    3. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. I. A. Cheltsov, K. A. Shramov, “Extremal Metrics on del Pezzo Threefolds”, Proc. Steklov Inst. Math., 264 (2009), 30–44  mathnet  crossref  mathscinet  isi  elib  elib
    6. Pukhlikov, AV, “Birational Geometry of Algebraic Varieties with a Pencil of Fano Cyclic Covers”, Pure and Applied Mathematics Quarterly, 5:2 (2009), 641  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Pukhlikov A.V., “Birational geometry of Fano hypersurfaces of index two”, Math. Ann., 366:1-2 (2016), 721–782  crossref  mathscinet  zmath  isi  elib  scopus
    9. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. Cheltsov I. Dubouloz A. Park J., “Super-Rigid Affine Fano Varieties”, Compos. Math., 154:11 (2018), 2462–2484  crossref  mathscinet  zmath  isi
    11. Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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