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Tr. Mat. Inst. Steklova, 2004, Volume 246, Pages 116–141 (Mi tm149)  

This article is cited in 15 scientific papers (total in 15 papers)

Mori Structures on a Fano Threefold of Index 2 and Degree 1

M. M. Grinenko

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: It is proved that the Mori structures on a nonsingular Fano threefold of index 2 and degree 1 are represented precisely by this Fano variety itself and by fibrations into del Pezzo surfaces of degree 1 that emerge from the blowups of curves of arithmetic genus 1 and degree 1. In particular, such a Fano variety is nonrational and all its birational automorphisms are regular.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 246, 103–128

Bibliographic databases:
UDC: 512.763
Received in February 2004

Citation: M. M. Grinenko, “Mori Structures on a Fano Threefold of Index 2 and Degree 1”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Tr. Mat. Inst. Steklova, 246, Nauka, MAIK Nauka/Inteperiodika, M., 2004, 116–141; Proc. Steklov Inst. Math., 246 (2004), 103–128

Citation in format AMSBIB
\Bibitem{Gri04}
\by M.~M.~Grinenko
\paper Mori Structures on a~Fano Threefold of Index~2 and Degree~1
\inbook Algebraic geometry: Methods, relations, and applications
\bookinfo Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences
\serial Tr. Mat. Inst. Steklova
\yr 2004
\vol 246
\pages 116--141
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm149}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2101287}
\zmath{https://zbmath.org/?q=an:1120.14031}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 246
\pages 103--128


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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. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. 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
    3. 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
    4. 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
    5. A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Hausen J., Herppich E., Suess H., “Multigraded Factorial Rings and Fano Varieties with Torus Action”, Doc Math, 16 (2011)  mathscinet  zmath  isi
    8. Debarre O., Iliev A., Manivel L., “On the Period Map for Prime Fano Threefolds of Degree 10”, J Algebraic Geom, 21:1 (2012), 21–59  crossref  mathscinet  zmath  isi  scopus
    9. A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150  mathnet  crossref  crossref  isi  elib
    10. Kishimoto T., Prokhorov Yu., Zaidenberg M., “Affine Cones Over Fano Threefolds and Additive Group Actions”, Osaka J. Math., 51:4 (2014), 1093–1112  mathscinet  zmath  isi
    11. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. 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
    13. Beauville A., “The Luroth Problem”, Rationality Problems in Algebraic Geometry, Lect. Notes Math., Lecture Notes in Mathematics, 2172, eds. Pardini R., Pirola G., Springer International Publishing Ag, 2016, 1–27  crossref  mathscinet  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. Cheltsov I., Dubouloz A., Park J., “Super-Rigid Affine Fano Varieties”, Compos. Math., 154:11 (2018), 2462–2484  crossref  mathscinet  zmath  isi
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