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Mat. Sb., 2005, Volume 196, Number 1, Pages 81–122 (Mi msb1262)  

This article is cited in 23 scientific papers (total in 23 papers)

On the degree of Fano threefolds with canonical Gorenstein singularities

Yu. G. Prokhorov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Fano threefolds $X$ with canonical Gorenstein singularities are considered. The sharp bound $-K_X^3\leqslant 72$ for their degree is proved.


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English version:
Sbornik: Mathematics, 2005, 196:1, 77–114

Bibliographic databases:

UDC: 512.7
MSC: 14J30, 14J45
Received: 02.12.2003 and 01.06.2004

Citation: Yu. G. Prokhorov, “On the degree of Fano threefolds with canonical Gorenstein singularities”, Mat. Sb., 196:1 (2005), 81–122; Sb. Math., 196:1 (2005), 77–114

Citation in format AMSBIB
\by Yu.~G.~Prokhorov
\paper On the degree of Fano threefolds with canonical Gorenstein singularities
\jour Mat. Sb.
\yr 2005
\vol 196
\issue 1
\pages 81--122
\jour Sb. Math.
\yr 2005
\vol 196
\issue 1
\pages 77--114

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    This publication is cited in the following articles:
    1. Yu. G. Prokhorov, “The degree of $\mathbb Q$-Fano threefolds”, Sb. Math., 198:11 (2007), 1683–1702  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Nill B., “Volume and lattice points of reflexive simplices”, Discrete Comput. Geom., 37:2 (2007), 301–320  crossref  mathscinet  zmath  isi  elib
    3. Yu. G. Prokhorov, “On Fano–Enriques threefolds”, Sb. Math., 198:4 (2007), 559–574  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Casagrande C., “Quasi-elementary contractions of Fano manifolds”, Compos. Math., 144:6 (2008), 1429–1460  crossref  mathscinet  zmath  isi
    5. Jahnke P., Peternell Th., “Almost del Pezzo manifolds”, Adv. Geom., 8:3 (2008), 387–411  crossref  mathscinet  zmath  isi
    6. Casagrande C., Jahnke P., Radloff I., “On the Picard number of almost Fano threefolds with pseudo-index $>1$”, Internat. J. Math., 19:2 (2008), 173–191  crossref  mathscinet  zmath  isi
    7. I. V. Karzhemanov, “On Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 200:8 (2009), 1215–1246  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Lopez A.F., Munoz R., Carlos Sierra J., “On the Extendability of Elliptic Surfaces of Rank Two and Higher”, Ann. Inst. Fourier, 59:1 (2009), 311–346  crossref  mathscinet  zmath  isi
    9. Kasprzyk A.M., “Canonical toric Fano threefolds”, Can. J. Math., 62:6 (2010), 1293–1309  crossref  mathscinet  zmath  isi
    10. Kaloghiros A.-S., “The Defect of Fano 3-Folds”, J Algebraic Geom, 20:1 (2011), 127–149  crossref  mathscinet  zmath  isi  elib
    11. G. D. Noce, “On the Picard Number of Singular Fano Varieties”, International Mathematics Research Notices, 2012  crossref  mathscinet  isi
    12. Mohammad Akhtar, Tom Coates, Sergey Galkin, Alexander M. Kasprzyk, “Minkowski Polynomials and Mutations”, SIGMA, 8 (2012), 094, 707 pp.  mathnet  crossref
    13. Casagrande C., “On the Birational Geometry of Fano 4-Folds”, Math. Ann., 355:2 (2013), 585–628  crossref  mathscinet  zmath  isi
    14. V. V. Przyjalkowski, “Weak Landau–Ginzburg models for smooth Fano threefolds”, Izv. Math., 77:4 (2013), 772–794  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. Gloria Della Noce, “A note on the Picard number of singular Fano 3-folds”, Geom Dedicata, 2013  crossref  mathscinet
    16. Coates T. Gonshaw S. Kasprzyk A. Nabijou N., “Mutations of Fake Weighted Projective Spaces”, Electron. J. Comb., 21:4 (2014)  mathscinet  zmath  isi
    17. Yu. G. Prokhorov, “On $G$-Fano threefolds”, Izv. Math., 79:4 (2015), 795–808  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. 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
    19. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    20. Lehmann B., Tanimoto Sh., “On Exceptional Sets in Manin'S Conjecture”, Res. Math. Sci., 6 (2018), 12  crossref  mathscinet  isi
    21. “P-Subgroups in the Space Cremona Group”, Math. Nachr., 291:8-9 (2018), 1374–1389  crossref  mathscinet  zmath  isi
    22. Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231  mathnet  crossref  crossref  isi
    23. Karzhemanov I., “Rationality of An S-6-Invariant Quartic 3-Fold”, Bull. Braz. Math. Soc., 51:1 (2020), 169–184  crossref  mathscinet  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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