Varieties whose hyperplane section are bundles
Maria Lucia Fania; Andrew John Sommese
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1988)
- Volume: 15, Issue: 2, page 193-218
- ISSN: 0391-173X
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topFania, Maria Lucia, and Sommese, Andrew John. "Varieties whose hyperplane section are $\mathbb {P}_\mathbb {C}^{\,k}$ bundles." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 15.2 (1988): 193-218. <http://eudml.org/doc/84029>.
@article{Fania1988,
author = {Fania, Maria Lucia, Sommese, Andrew John},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {projective bundle; 4-folds; hyperplane section; extension of holomorphic map; ample and spanned line bundle},
language = {eng},
number = {2},
pages = {193-218},
publisher = {Scuola normale superiore},
title = {Varieties whose hyperplane section are $\mathbb \{P\}_\mathbb \{C\}^\{\,k\}$ bundles},
url = {http://eudml.org/doc/84029},
volume = {15},
year = {1988},
}
TY - JOUR
AU - Fania, Maria Lucia
AU - Sommese, Andrew John
TI - Varieties whose hyperplane section are $\mathbb {P}_\mathbb {C}^{\,k}$ bundles
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1988
PB - Scuola normale superiore
VL - 15
IS - 2
SP - 193
EP - 218
LA - eng
KW - projective bundle; 4-folds; hyperplane section; extension of holomorphic map; ample and spanned line bundle
UR - http://eudml.org/doc/84029
ER -
References
top- [A+K] A. Altman - S. Kleiman, Introduction to Grothendieck Duality Theory, Springer Lecture Notes146 (1970), Springer Verlag, Berlin. Zbl0215.37201MR274461
- [B1] L Bådescu, On ample divisors II, Proceedings of the "Week of Algebraic Geometry", Bucharest 1980, Teubner, Leipzig1981. Zbl0493.14003MR712511
- [B2] L Bådescu, On ample divisors, Nagoya Math. Journal86 (1982), pp. 155-171. Zbl0445.14002MR661223
- [B3] L Bådescu, Hyperplane sections and deformations, Algebraic Geometry, Springer Lecture Notes1056 (1984), pp. 1-33, Springer Verlag, Berlin. Zbl0539.14004MR749936
- [D+M] M. Deschamps - L. Menegaux, Surfaces de type general dominees par une variete fixe, C.R. Acad Sci. Paris Ser. A-B291 (1980). Zbl0453.14014MR600002
- [E] R. Elkik, Singularites rationelles et deformations, Inv. Math., 47 (1978), pp. 139-147. Zbl0363.14002MR501926
- [Fa1] M.L. Fania, Extension of modifications of ample divisors on fourfolds, J. Math. Soc. Japan, 36 (1984), pp. 107-120. Zbl0513.14004MR723597
- [Fa2] M.L. Fania, Extension of modifications of ample divisors on fourfolds II, J. Math. Soc. Japan, 38 (1986), pp. 285-294. Zbl0597.14035MR833203
- [Fa+So] M.L. Fania - A.J. Sommese, On the minimality of hyperplane sections of Gorenstein 3-folds, Proceedings in honor of W. Stoll, Notre Dame (1984), Aspects of MathematicsE9 (1986), pp. 89-114, Vieweg. Zbl0595.14030MR859194
- [F+S+So] M.L. Fania - E. Sato - A.J. Sommese, On the structure of fourfolds with a hyperplane section which is a P1 bundle over a surface that fibres over a curve, Nagoya Math. Journal, 108 (1987), pp. 1-14. Zbl0602.14014MR920324
- [Fu1] T. Fujita, On the hyperplane section principle of Lefschetz, J. Math. Soc. Japan32 (1980), pp. 153-169. Zbl0414.14007MR554521
- [Fu2] T. Fujita, Rational retractions onto ample divisors, Sci. Papers of the College of Arts and Sciences of the University of Tokyo33 (1983), pp. 33-39. Zbl0518.14005MR714669
- [(G+M)1] M. Goresky - R. Macpherson, On the topology of complex algebraic maps, to appear. Zbl0525.14010MR708330
- [(G+M)2] M. Goresky - R. Macpherson, Stratified Morse theory, Proceedings of Symposia in Pure Mathematics40 (1983), part 1, pp. 517-533. Zbl0526.57022MR713089
- [(G+M)3] M. Goresky - R. Macpherson, Morse theory and intersection homology, Analyse et Topologie sur les Espace Singuliers, Asterique101 (1983), pp. 135-192. Zbl0524.57022MR737930
- [Gr+Ri] H. Grauert - O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Raumen, Inv. Math.11 (1970), pp. 263-292. Zbl0202.07602MR302938
- [Gri] P.A. Griffiths, The extension problem in complex analysis II, Amer. J. Math.88 (1966), pp. 366-446. Zbl0147.07502MR206980
- [Gro] A. Grothendieck, Cohomologie locale des faisceaux coherents et theoremes de Lefschetz locaux et globaux (DGA 2), North Holland Press. Zbl0197.47202
- [H] H.A. Hamm, Lefschetz theorems for singular varieties, Proc. Symp. in Pure Math. 40-1 (1983), pp. 547-557. Zbl0525.14011MR713091
- [Ha] R. Hartshorne, Algebraic Geometry, Springer Verlag, Berlin-Heidelberg- New York, 1977. Zbl0367.14001MR463157
- [Ka] Y. Kawamata, A generalization of Kodaira-Ramanujam's vanishing theorem, Math. Ann.261 (1982), pp. 43-46. Zbl0476.14007MR675204
- [Ke] G. Kempf et al., Toroidal embeddings I, Springer Lecture Notes339 (1973), Springer Verlag, Berlin. Zbl0271.14017MR335518
- [LP] J. Le Potier, Problemes d' extension de classes de cohomologie, Seminaire de geometrie analytique, Asterique17 (1979), pp. 79-109. Zbl0308.32020MR387668
- [M] K. Maehara, Family of varieties dominated by a variety, Proc. Japan Acad. Ser. A, Math. Sci.55 (1979), pp. 146-151. Zbl0432.14003MR533710
- [Ro] L. Roth, Algebraic Threefolds, Springer Verlag, Berlin (1953).
- [Sh+So] B. Shiffman - A.J. Sommese, Vanishing Theorems on Complex Manifolds, Progress in Mathematics56 (1985), Birkhauser, Boston. Zbl0578.32055MR782484
- [Si] A. Silva, Relative vanishing theorems 1: applications to ample divisors, Comm. Math. Helv.52 (1977), pp. 483-489. Zbl0372.32014MR460733
- [So1] A.J. Sommese, On manifolds that cannot be ample divisors, Math. Ann.221 (1976), pp. 55-72. Zbl0306.14006MR404703
- [So2] A.J. Sommese, On the minimality of hyperplane sections of projective threefolds, J. reine und angew. Math.329 (1981), pp. 16-41. Zbl0509.14044MR636441
- [So3] A.J. Sommese, Ample divisors on 3-folds, Algebraic Threefolds, Springer Lecture Notes947 (1982), pp. 229-240. Zbl0494.14016MR672620
- [So4] A.J. Sommese, On the birational theory of hyperplane sections of projective threefolds, Unpublished 1981 Manuscript. MR644822
- [So5] A.J. Sommese, Complex subspaces of homogeneous complex manifolds, II-Homotopy results, Nagoya Math. J.86 (1982), pp. 101-129. Zbl0497.32026MR661221
- [So6] A.J. Sommese, On the adjunction theoretic structure of projective varieties, Proceedings of Complex Geometry Conference, Göttingen, May 1985 (ed. by H. Grauert), Springer Lecture Notes in Mathematics1164 (1986), pp. 175-213. Zbl0601.14029MR855885
- [V] E. Viehweg, Vanishing theorems, J. reine und angew. Math.335 (1982), pp. 1-8. Zbl0485.32019MR667459
- [W] R.O. Wells, Comparison of de Rham and Dolbeault cohomology for proper surjective mappings, Pac. Jour. of Math.53 (1974), pp. 281-300. Zbl0261.32005MR367307
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