Del Pezzo surfaces as hyperplane sections

Antonio LANTERI; Marino PALLESCHI; Andrew J. SOMMESE

doi:10.2969/jmsj/04930501

Antonio LANTERI, Marino PALLESCHI, Andrew J. SOMMESE

著者情報

ジャーナルフリー

1997 年 49 巻 3 号 p. 501-529

DOI https://doi.org/10.2969/jmsj/04930501

詳細

Published: 1997 Received: 1994/08/03 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Dipartimento di Matematicà “F. Enriques”.University
2) Department of Mathematics University of Notre Dame

訂正後 :
1) Dipartimento di Matematica “F. Enriques”-Università
2) Department of Mathematics University of Notre Dame

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : Ba1) L. Badescu, On ample divisors, Nagoya Math. J., 86 (1982), 155-171.
Ba2) L. Badescu, The projective plane blown-up at a point as an ample divisor, Atti Acc. Ligure Sci. Lett., 38 (1982), 88-92.
BS) M. C. Beltrametti and A. J. Sommese, New properties of special varieties arising from adjunction theory, J. Math. Soc. Japan, 43 (1991), 381-412.
BS1) M. C. Beltrametti and A. J. Sommese, The Adjunction Theory of Complex Projective Varieties, Expositions in Math., vol. 16, De Gruyter, 1995.
Fu) T. Fujita, On the structure of polarized manifolds with total deficiency one, I, II, III, J. Math. Soc. Japan, 32 (1980), 709-725; 33 (1981), 415-434; 36 (1984), 75-89.
Fu1) T. Fujita, Classification of polarized manifolds of sectional genus two, Algebraic geometry and Commutative Algebra, in Honor of M. Nagata, pp. 73-98, Kino-kuniya, 1987.
Fu2) T. Fujita, Classification Theories of Polarized Varieties, London Math. Soc. Lect. Note Series 155, Cambridge Univ. Press, Cambridge, 1990.
FSaSo) M. L. Fania, E. Sato and A. J. Sommese, On the structure of 4-folds with a hyperplane section which is a P¹-bundle over a surface that fibres over a curve, Nagoya Math. J., 108 (1987), 1-14.
Ha) J. Harris, A bound on the geometric genus of projective varieties, Ann. Sc. Norm. Sup. Pisa, (4)8 (1981), 35-68.
Io) P. Ionescu, Embedded projective varieties of small invariants, Algebraic Geometry, Proc. Bucharest 1982, pp. 142-186, Lect. Notes Math., 1056, Springer-Verlag, Berlin, Heidelberg, New York, 1984.
Is) V. A. Iskovskih, Fano 3-folds, I. Math. U. S. S. R. Izvestija, 11 (1977), 485-527.
LPS) A. Lanteri, M. Palleschi and A. J. Sommese, Double covers of Pⁿ as very ample divisors. Nagoya Math. J., 137 (1995), 1-32.
LPS1) A. Lanteri, M. Palleschi and A. J. Sommese, On triple covers of Pⁿ as very ample divisors, Classification of Algebraic Varieties, Proceedings L'Aquila 1992, Contemporary Mathematics, 162, pp. 277-292, Amer. Math. Soc., 1994.
KO) S. Kobayashi and T. Ochiai, Characterizations of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ., 13 (1973), 31-47.
Sa) E. Sato, Varieties which have two projective space bundle structures, J. Math. Kyoto Univ., 25 (1985), 445-457.
S1) A. J. Sommese, On manifolds that cannot be ample divisors, Math. Ann., 221 (1976), 55-72.
S2) A. J. Sommese, On the adjunction theoretic structure of projective varieties, Complex Analysis and Algebraic Geometry, Proc. Gottingen 1985, pp. 175-213, Lect. Notes Math., 1194, Springer-Verlag, Berlin, Heidelberg, New York, 1986.
S3) A. J. Sommese, On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold, J. reine angew. Math., 402 (1989), 220-221; Erratum, ibidem, 411 (1989), 122-123.
SV) A. J. Sommese and A. van de Ven, On the adjunction mapping, Math. Ann., 278 (1987), 593-603.
SzW) M. Szurek and J. A. Wisniewski, Fano bundles of rank 2 on surfaces, Compositio Math., 76 (1990), 295-305.

Right : [Ba1] L. Badescu, On ample divisors, Nagoya Math. J., 86 (1982), 155-171.
[Ba2] L. Badescu, The projective plane blown-up at a point as an ample divisor, Atti Acc. Ligure Sci. Lett., 38 (1982), 88-92.
[BS] M. C. Beltrametti and A. J. Sommese, New properties of special varieties arising from adjunction theory, J. Math. Soc. Japan, 43 (1991), 381-412.
[BS1] M. C. Beltrametti and A. J. Sommese, The Adjunction Theory of Complex Projective Varieties, Expositions in Math., vol. 16, De Gruyter, 1995.
[Fu] T. Fujita, On the structure of polarized manifolds with total deficiency one, I, II, III, J. Math. Soc. Japan, 32 (1980), 709-725; 33 (1981), 415-434; 36 (1984), 75-89.
[Fu1] T. Fujita, Classification of polarized manifolds of sectional genus two, Algebraic geometry and Commutative Algebra, in Honor of M. Nagata, pp. 73-98, Kino-kuniya, 1987.
[Fu2] T. Fujita, Classification Theories of Polarized Varieties, London Math. Soc. Lect. Note Series 155, Cambridge Univ. Press, Cambridge, 1990.
[FSaSo] M. L. Fania, E. Sato and A. J. Sommese, On the structure of 4-folds with a hyperplane section which is a P¹-bundle over a surface that fibres over a curve, Nagoya Math. J., 108 (1987), 1-14.
[Ha] J. Harris, A bound on the geometric genus of projective varieties, Ann. Sc. Norm. Sup. Pisa, (4) 8 (1981), 35-68.
[Io] P. Ionescu, Embedded projective varieties of small invariants, Algebraic Geometry, Proc. Bucharest 1982, pp. 142-186, Lect. Notes Math., 1056, Springer-Verlag, Berlin, Heidelberg, New York, 1984.
[Is] V. A. Iskovskih, Fano 3-folds, I. Math. U. S. S. R. Izvestija, 11 (1977), 485-527.
[LPS] A. Lanteri, M. Palleschi and A. J. Sommese, Double covers of Pⁿ as very ample divisors. Nagoya Math. J., 137 (1995), 1-32.
[LPS1] A. Lanteri, M. Palleschi and A. J. Sommese, On triple covers of Pⁿ as very ample divisors, Classification of Algebraic Varieties, Proceedings L'Aquila 1992, Contemporary Mathematics, 162, pp. 277-292, Amer. Math. Soc., 1994.
[KO] S. Kobayashi and T. Ochiai, Characterizations of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ., 13 (1973), 31-47.
[Sa] E. Sato, Varieties which have two projective space bundle structures, J. Math. Kyoto Univ., 25 (1985), 445-457.
[S1] A. J. Sommese, On manifolds that cannot be ample divisors, Math. Ann., 221 (1976), 55-72.
[S2] A. J. Sommese, On the adjunction theoretic structure of projective varieties, Complex Analysis and Algebraic Geometry, Proc. Gottingen 1985, pp. 175-213, Lect. Notes Math., 1194, Springer-Verlag, Berlin, Heidelberg, New York, 1986.
[S3] A. J. Sommese, On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold, J. reine angew. Math., 402 (1989), 220-221; Erratum, ibidem, 411 (1989), 122-123.
[SV] A. J. Sommese and A. van de Ven, On the adjunction mapping, Math. Ann., 278 (1987), 593-603.
[SzW] M. Szurek and J. A. Wisniewski, Fano bundles of rank 2 on surfaces, Compositio Math., 76 (1990), 295-305.

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