Extension of modifications of ample divisors on fourfolds

Maria Lucia FANIA

doi:10.2969/jmsj/03610107

Maria Lucia FANIA

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JOURNAL FREE ACCESS

1984 Volume 36 Issue 1 Pages 107-120

DOI https://doi.org/10.2969/jmsj/03610107

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Published: 1984 Received: September 20, 1982 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Andreotti and T. Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math., 69 (1959), 713-717.
2) G. Fischer, Complex analytic geometry, Lecture Notes in Math., 538, Springer-Verlag, Berlin-Heidelberg-New York, 1976.
3) T. Fujita, On the hyperplane section principle of Lefschetz, J. Math. Soc. Japan, 32 (1980), 153-169.
4) Gunning-Rossi, Analytic functions of several complex variables, Prentice-Hall, 1965.
5) R. Hartshorne, Algebraic geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
6) R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Math., 156, Springer-Verlag, Berlin-Heidelberg-New York, 1970.
7) H. Hironaka, Smoothing of algebraic cycles of small dimensions, Amer. J. Math., 90 (1968), 1-54.
8) B. G. Moisenzon, The Castelnuovo-Enriques contraction theorem for arbitrary dimension, Izv. Acad. Nauk SSSR Ser. Math., 33(1969), 974-1025.
9) D. Mumford, Pathologies III, Amer. J. Math., 89(1967), 94-104.
10) C. P. Ramanujam, Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc., 36(1972), 41-51.
11) G. Scorza, Sulle varieta di Segre, Opere Scelte, Vol. I, 376-386.
12) Unpublished notes by B. Shiffman and A. J. Sommese.
13) A. J. Sommese, On the minimality of hyperplane sections of projective threefolds, J. Reine Angew. Math., 329 (1981), 16-41.
14) A. J. Sommese, On manifolds that cannot be ample divisors, Math. Ann., 221(1976), 55-72.
15) A. J. Sommese, Hyperplane sections of projective surfaces; I-the adjunction mapping, Duke Math. J., 46(1979), 377-401.
16) A. J. Sommese, The birational theory of hyperplane sections of projective threefolds, to appear.
17) N. Steenrod, The Topology of fibre bundles, Princeton University Press, 1951.
18) K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Math., 439, Springer-Verlag, Berlin-Heidelberg-New York, 1975.

Right : [1] A. Andreotti and T. Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math., 69 (1959), 713-717.
[2] G. Fischer, Complex analytic geometry, Lecture Notes in Math., 538, Springer-Verlag, Berlin-Heidelberg-New York, 1976.
[3] T. Fujita, On the hyperplane section principle of Lefschetz, J. Math. Soc. Japan, 32 (1980), 153-169.
[4] Gunning-Rossi, Analytic functions of several complex variables, Prentice-Hall, 1965.
[5] R. Hartshorne, Algebraic geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
[6] R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Math., 156, Springer-Verlag, Berlin-Heidelberg-New York, 1970.
[7] H. Hironaka, Smoothing of algebraic cycles of small dimensions, Amer. J. Math., 90 (1968), 1-54.
[8] B. G. Moisenzon, The Castelnuovo-Enriques contraction theorem for arbitrary dimension, Izv. Acad. Nauk SSSR Ser. Math., 33 (1969), 974-1025.
[9] D. Mumford, Pathologies III, Amer. J. Math., 89 (1967), 94-104.
[10] C. P. Ramanujam, Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc., 36 (1972), 41-51.
[11] G. Scorza, Sulle varieta di Segre, Opere Scelte, Vol. I, 376-386.
[12] Unpublished notes by B. Shiffman and A. J. Sommese.
[13] A. J. Sommese, On the minimality of hyperplane sections of projective threefolds, J. Reine Angew. Math., 329 (1981), 16-41.
[14] A. J. Sommese, On manifolds that cannot be ample divisors, Math. Ann., 221 (1976), 55-72.
[15] A. J. Sommese, Hyperplane sections of projective surfaces; I-the adjunction mapping, Duke Math. J., 46 (1979), 377-401.
[16] A. J. Sommese, The birational theory of hyperplane sections of projective threefolds, to appear.
[17] N. Steenrod, The Topology of fibre bundles, Princeton University Press, 1951.
[18] K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Math., 439, Springer-Verlag, Berlin-Heidelberg-New York, 1975.

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