On the hyperplane section principle of Lefschetz

Takao FUJITA

doi:10.2969/jmsj/03210153

Takao FUJITA

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1980 Volume 32 Issue 1 Pages 153-169

DOI https://doi.org/10.2969/jmsj/03210153

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Published: 1980 Received: June 05, 1978 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) M. Artin, Algebraization of formal moduli II, Existence of modifications, Ann. of Math., 91 (1970), 88-135.
2) W. Barth, Subvarieties of low codimension in projective space, Int. Cong. of Math. at Vancouver Lect.
3) T. Fujita, On the structure of polarized varieties with Δ-genera zero, J. Fac. Sci. Univ. Tokyo, 22 (1975), 103-115.
4) T. Fujita, Defining equations for certain types of polarized varieties, Complex Analysis and Algebraic Geometry, Tokyo, Iwanami, 1977.
5) T. Fujita, On the structure of certain types of polarized varieties I and II, Proc. Japan Acad., 49 (1973), 800-802 and ibid., 50 (1974), 411-412.
6) T. Fujita, On the structure of polarized manifolds with total deficiency one, preprint.
7) T. Fujita, Defining equations for certain types of polarized varieties over a field of positive characteristic, in preparation.
8) A. Grothendieck, Eléments de géométrie algébrique, Publ. Math. I. H. E. S., 4, 8,11 and 17.
9) R. Hartshorne, Residue and Duality, Lecture Notes in Math., 20, Springer,1966.
10) R. Hartshorne, Ample Vector Bundles, Publ. Math. I. H. E. S., 29 (1966), 319-349.
11) R. Hartshorne, Ample Subvarieties of Algebraic Varieties, Lecture Notes in Math,,156, Springer, 1970.
12) R. Hartshorne, Varieties of small codimension in projective space, Bull. Amer. Math. Soc., 80 (1974), 1-17-1032.
13) K. Kodaira and J. Morrow, Complex Manifolds, New York, Holt, Rinehart & Winston, 1971.
14) J. Milnor, Morse Theory, Princeton Univ. Press, 1963.
15) B. G. Moisezon, On n-dimensional compact varieties with n algebraically independent meromorphic functions I, II & III, Izv. Akad. Nauk SSSR Ser. Math., 30 (1966), 133-174, 345-386 and 621-656. AMS translations Ser. 2, 63, 51-177.
16) B.G. Moisezon, The Castelnuovo-Enriques contraction theorem for arbitrary dimension, (Russian), Izv. Acad. Nauk SSSR Ser. Math., 33 (1969), 974-1025.
17) S. Mori, On a generalization of complete intersections, J. Math. Kyoto Univ., 15 (1975), 619-646.
18) D. Mumford, Pathology III, Amer. J. Math., 89 (1967), 94-103.
19) D. Mumford, Varieties defined by quadratic equations, Questioni sulle varieta algebriche, Corsi dal C. I. M. E. Edizioni Cremonese, Roma, 1969.
20) M. Nagata, On rational surfaces I and II, Mem. Coll. Sci. Univ. Kyoto, 32 (1960), 351-370 and 33 (1961), 271-293.
21) Y, Nakai, A criterion of an ample sheaf on a projective scheme, Amer. J. Math., 85 (1963), 14-26.
22) C.P. Ramanujam, Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc. (N. S.), 36 (1972), 41-51.
23) J. P. Serre, Faisceaux algébriques cohérents, Ann. of Math., 61 (1955), 197-278.
24) A. J. Sommese, On manifolds that cannot be ample divisors, Math. Ann., 221 (1976), 55-72.

Right : [1] M. Artin, Algebraization of formal moduli II, Existence of modifications, Ann. of Math., 91 (1970), 88-135.
[2] W. Barth, Subvarieties of low codimension in projective space, Int. Cong. of Math. at Vancouver Lect.
[3] T. Fujita, On the structure of polarized varieties with Δ-genera zero, J. Fac. Sci. Univ. Tokyo, 22 (1975), 103-115.
[4] T. Fujita, Defining equations for certain types of polarized varieties, Complex Analysis and Algebraic Geometry, Tokyo, Iwanami, 1977.
[5] T. Fujita, On the structure of certain types of polarized varieties I and II, Proc. Japan Acad., 49 (1973), 800-802 and Proc. Japan Acad., 50 (1974), 411-412.
[6] T. Fujita, On the structure of polarized manifolds with total deficiency one, preprint.
[7] T. Fujita, Defining equations for certain types of polarized varieties over a field of positive characteristic, in preparation.
[8] A. Grothendieck, Eléments de géométrie algébrique, Publ. Math. I. H. E. S., 4, 8,11 and 17.
[9] R. Hartshorne, Residue and Duality, Lecture Notes in Math., 20, Springer,1966.
[10] R. Hartshorne, Ample Vector Bundles, Publ. Math. I. H. E. S., 29 (1966), 319-349.
[11] R. Hartshorne, Ample Subvarieties of Algebraic Varieties, Lecture Notes in Math,,156, Springer, 1970.
[12] R. Hartshorne, Varieties of small codimension in projective space, Bull. Amer. Math. Soc., 80 (1974), 1-17-1032.
[13] K. Kodaira and J. Morrow, Complex Manifolds, New York, Holt, Rinehart & Winston, 1971.
[14] J. Milnor, Morse Theory, Princeton Univ. Press, 1963.
[15] B. G. Moisezon, On n-dimensional compact varieties with n algebraically independent meromorphic functions I, II & III, Izv. Akad. Nauk SSSR Ser. Math., 30 (1966), 133-174, 345-386 and 621-656. AMS translations Ser. 2, 63, 51-177.
[16] B. G. Moisezon, The Castelnuovo-Enriques contraction theorem for arbitrary dimension, (Russian), Izv. Acad. Nauk SSSR Ser. Math., 33 (1969), 974-1025.
[17] S. Mori, On a generalization of complete intersections, J. Math. Kyoto Univ., 15 (1975), 619-646.
[18] D. Mumford, Pathology III, Amer. J. Math., 89 (1967), 94-103.
[19] D. Mumford, Varieties defined by quadratic equations, Questioni sulle varieta algebriche, Corsi dal C. I. M. E. Edizioni Cremonese, Roma, 1969.
[20] M. Nagata, On rational surfaces I and II, Mem. Coll. Sci. Univ. Kyoto, 32 (1960), 351-370 and 33 (1961), 271-293.
[21] Y, Nakai, A criterion of an ample sheaf on a projective scheme, Amer. J. Math., 85 (1963), 14-26.
[22] C. P. Ramanujam, Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc. (N. S.), 36 (1972), 41-51.
[23] J. P. Serre, Faisceaux algébriques cohérents, Ann. of Math., 61 (1955), 197-278.
[24] A. J. Sommese, On manifolds that cannot be ample divisors, Math. Ann., 221 (1976), 55-72.

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