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Halphen pencils on weighted Fano threefold hypersurfaces

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EN
Abstrakty
EN
On a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.
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Bibliografia
  • [1] Cheltsov I., Elliptic structures on weighted three-dimensional Fano hypersurfaces, Izv. Ross. Akad. Nauk Ser. Mat., 2007, 71, 765–862 (in Russian)
  • [2] Cheltsov I., Park J., Weighted Fano threefold hypersurfaces, J. Reine Angew. Math., 2006, 600, 81–116
  • [3] Cheltsov I., Park J., Halphen Pencils on weighted Fano threefold hypersurfaces (extended version), preprint available at arXiv:math/0607776 [WoS]
  • [4] Corti A., Singularities of linear systems and 3-fold birational geometry, London Math. Soc. Lecture Note Ser., 2000, 281, 259–312
  • [5] Corti A., Pukhlikov A., Reid M., Fano 3-fold hypersurfaces, London Math. Soc. Lecture Note Ser., 2000, 281, 175–258
  • [6] Dolgachev I.V., Rational surfaces with a pencil of elliptic curves, Izv. Akad. Nauk SSSR Ser. Mat., 1966, 30, 1073–1100 (in Russian)
  • [7] Kawamata Y., Divisorial contractions to 3-dimensional terminal quotient singularities, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, 241–246
  • [8] Kawamata Y., Matsuda K., Matsuki K., Introduction to the minimal model problem, Advanced Studies in Pure Mathematics, 1987, 10, 283–360
  • [9] Ryder D., Classification of elliptic and K3 fibrations birational to some ℚ-Fano 3-folds, J. Math. Sci. Univ. Tokyo, 2006, 13, 13–42
  • [10] Ryder D., The Curve Exclusion Theorem for elliptic and K3 fibrations birational to Fano 3-fold hypersurfaces, preprint available at arXiv:math.AG/0606177 [WoS]
  • [11] Shokurov V.V., Three-dimensional log perestroikas, Izv. Ross. Akad. Nauk Ser. Mat., 1993, 40, 95–202 http://dx.doi.org/10.1070/IM1993v040n01ABEH001862[Crossref]
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0056-2
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