On the Birationality of the Bicanonical Map of a Surface Section of a Threefold

References

• Beltrametti , M. C. , Sommese , A. J. ( 1995a ). On the dimension of the adjoint linear system for threefolds . Ann. Scuola Norm. Sup. Pisa Cl. Sci. Ser. XXII ( 4 ): 1 – 24 .
   Google Scholar
• Beltrametti , M. C. , Sommese , A. J. ( 1995b ). The Adjunction Theory of Complex Projective Varieties . Expositions in Mathematics 16 . W. de Gruyter .
   Google Scholar
• Beltrametti , M. C. , Sommese , A. J. ( 1997 ). On the second adjunction mapping. The case of a 1-dimensional image . Trans. Amer. Math. Soc. 349 ( 8 ): 3277 – 3302 .
   Google Scholar
• Beltrametti , M. C. , Sommese , A. J. ( 1999a ). On the degree and the birationality of the second adjunction mapping . Internat. J. Math. 10 : 707 – 719 .
   Google Scholar
• Beltrametti , M. C. , Sommese , A. J. (1999b). Projective manifolds with small pluridegrees. Trans. Amer. Math. Soc. 352(7):3045–3064.
   Google Scholar
• Beltrametti , M. C. , Sommese , A. J. ( 2001 ). On the bicanonical map of a surface section of a threefold . Abh. Math. Sem. Univ. Hamburg 71 : 269 – 277 .
   Google Scholar
• Beltrametti , M. C. , Schneider , M. , Sommese , A. J. ( 1995 ). Some special properties of the adjunction theory for 3-folds in ℙ5 . Memoirs of A.M.S. 116 ( 554 ).
   Google Scholar
• Calabri , A. , Ferraro , R. ( 2002 ). Explicit resolutions of double point singularities of surfaces . Collect. Math. 53 : 99 – 131 .
   Google Scholar
• Ciliberto , C. ( 1997 ). The bicanonical map for surfaces of general type . Proc. Symp. Pure Math. 62 ( I ): 57 – 84 .
   Google Scholar
• Ciliberto , C. , Francia , P. , Mendes Lopez , M. ( 1997 ). Remarks on the bicanonical map for surfaces of general type . Math. Z. 224 : 137 – 166 .
   Web of Science ®Google Scholar
• Du Val , P. ( 1952 ). On surfaces whose canonical system is not hyperelliptic . Canadian J. of Math. 4 : 204 – 221 .
   Google Scholar
• Fujita , T. ( 1984 ). On the structure of polarized manifolds with total deficiency one, Part III . J. Math. Soc. Japan 32 : 75 – 89 .
   Google Scholar
• Fujita , T. ( 1989 ). Remarks on quasi-polarized varieties . Nagoya Math. J. 115 : 105 – 123 .
   Google Scholar
• Harris , J. ( 1982 ). Curves in Projective Space , with the collaboration of D. Eisenbud, Université de Montreal, Montreal (Québec), Canada .
   Google Scholar
• Iskovskih , V. A. ( 1977 ). Fano threefolds . I. Math. USSR Izvestija 11 : 485 – 527 .
   Web of Science ®Google Scholar
• Kawamata , Y. , Matsuda , K. , Matsuki , K. ( 1987 ). Introduction to the minimal model problem . Algebraic Geometry, Sendai 1985 . Kinokunya Co. Ltd. Tokyo. Adv. Stud. Pure Math. 10 , pp. 283 – 360 .
   Google Scholar
• Lanteri , A. , Palleschi , M. , Sommese , A. J. ( 1994 ). On triple covers of ℙ n as very ample divisors . In: Ciliberto , C. , Livorni , E. L. , Sommese , A. J. , eds. Classification of Algebraic Varieties, Proceedings, L'Aquila, 1992 . Contemp. Math. , pp. 277 – 292 .
   Google Scholar
• Sommese , A. J. ( 1997 ). What we know about the second adjunction mapping . Rend. Sem. Mat. Fis. Milano 67 : 49 – 75 .
   Google Scholar
• Tsuji , H. ( 1988 ). Stability of tangent bundles of minimal algebraic varieties . Topology 27 : 429 – 442 .
   Web of Science ®Google Scholar
• Communicated by C. Pedrini.
   Google Scholar