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2011 | 9 | 3 | 449-488

Tytuł artykułu

Threefolds with big and nef anticanonical bundles II

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Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
In a follow-up to our paper [Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631], we classify smooth complex projective threefolds Xwith −K X big and nef but not ample, Picard number γ(X) = 2, and whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop X + are not both birational.

Wydawca

Czasopismo

Rocznik

Tom

9

Numer

3

Strony

449-488

Opis fizyczny

Daty

wydano
2011-06-01
online
2011-03-22

Twórcy

  • Freie Universität Berlin
  • Universität Bayreuth
autor
  • Universität Bayreuth

Bibliografia

  • [1] Arbarello E., Cornalba M., Griffiths P.A., Harris J., Geometry of Algebraic Curves, Grundlehren Math. Wiss., 267, Springer, New York, 1985
  • [2] Bertini E., Introduzione alla Geometria Proiettiva degli Iperspazi, Enrico Spoerri, Pisa, 1907
  • [3] Chel’tsov I.A., Bounded three-dimensional Fano varieties of integer index, Math. Notes, 1999, 66(3), 360–365 http://dx.doi.org/10.1007/BF02676446
  • [4] Hartshorne R., On the classification of algebraic space curves II, In: Algebraic Geometry, Brunswick, 1985, Proc. Sympos. Pure Math., 46(1), AMS, Providence, 1987, 145–164
  • [5] Iskovskikh V.A., Double projection from a line onto Fano threefolds of the first kind, Math. USSR-Sb., 1990, 66(1), 265–284 http://dx.doi.org/10.1070/SM1990v066n01ABEH001172
  • [6] Iskovskikh V.A., Prokhorov Yu.G., Fano Varieties, Encyclopaedia Math. Sci., 47, Springer, Berlin, 1999
  • [7] Jahnke P., Peternell T., Almost del Pezzo manifolds, Adv. Geom., 2008, 8(3), 387–411 http://dx.doi.org/10.1515/ADVGEOM.2008.026
  • [8] Jahnke P., Peternell T., Radloff I., Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631 http://dx.doi.org/10.1007/s00208-005-0682-y
  • [9] Jahnke P., Radloff I., Gorenstein Fano threefolds with base points in the anticanonical system. Compos. Math., 2006, 142(2), 422–432 http://dx.doi.org/10.1112/S0010437X05001673
  • [10] Jahnke P., Radloff I., Terminal Fano threefolds and their smoothings, Math. Z. (in press), DOI: 10.1007/s00209-010-0780-8
  • [11] Kollár J., Flops, Nagoya Math. J., 1989, 113, 15–36
  • [12] Kollár J., Flips, flops, minimal models, etc., In: Surv. Differ. Geom., 1, Lehigh University, Bethlehem, 1991, 113–199
  • [13] Kollár J., Mori S., Birational Geometry of Algebraic Varieties, Cambridge Tracts in Math., 134, Cambridge University Press, Cambridge, 1998
  • [14] Mori S., Threefolds whose canonical bundles are not numerically effective, Ann. of Math., 1982, 116(1), 133–176 http://dx.doi.org/10.2307/2007050
  • [15] Namikawa Y., Smoothing Fano 3-folds. J. Algebraic Geom., 1997, 6(2), 307–324
  • [16] Przhyjalkowski V.V., Cheltsov I.A., Shramov K.A., Hyperelliptic and trigonal Fano threefolds, Izv. Math., 2005, 69(2), 365–421 http://dx.doi.org/10.1070/IM2005v069n02ABEH000533
  • [17] Reid M., Minimal models of canonical 3-folds, In: Algebraic Varieties and Analytic Varieties, Tokyo, 1981, Adv. Stud. Pure Math., 1, North-Holland, Amsterdam, 1983, 131–180
  • [18] Shin K.-H., 3-dimensional Fano varieties with canonical singularities. Tokyo J. Math., 1989, 12(2), 375–385 http://dx.doi.org/10.3836/tjm/1270133187
  • [19] Takeuchi K., Some birational maps of Fano 3-folds, Compos. Math., 1989, 71(3), 265–283

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_2478_s11533-011-0023-1
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