Halphen pencils on weighted Fano threefold hypersurfaces

• Autorzy: Ivan Cheltsov , Jihun Park
• Języki publikacji: 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.

Słowa kluczowe

EN

Fano threefolds; Weighted hypersurfaces; K3 surfaces; Halphen pencils; Birational automorphisms

Kategorie tematyczne

• 14E07: Birational automorphisms, Cremona group and generalizations
• 14J28: K 3 surfaces and Enriques surfaces
• 14J70: Hypersurfaces
• 14J45: Fano varieties
• 14D06: Fibrations, degenerations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 1
• Strony: 1-45

Daty

wydano

2009-03-01

online

2009-01-10

Twórcy

autor

Ivan Cheltsov

• School of Mathematics, The University of Edinburgh, Edinburgh, UK

autor

Jihun Park

• Department of Mathematics, POSTECH, Pohang, Korea

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]
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• [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]
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Identyfikatory

DOI

10.2478/s11533-008-0056-2