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On the Hyperplane Sections of Blow-Ups of Complex Projective Plane

Published online by Cambridge University Press:  20 November 2018

Aldo Biancofiore
Aldo Biancofiore*
Affiliation:
Via Roma, L'Aquila, Italy
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Let L be a line bundle on a connected, smooth, algebraic, projective surface X. In this paper we have studied the following questions:

1) Under which conditions is L spanned by global sections? I.e., if ɸL : X →PN denotes the map associated to the space Г(L) of the sections of L, when is ɸL a morphism?

2) Under which conditions is L very ample? I.e., when does ɸL give an embedding?

These problems arise naturally in the study, and in particular in the classification, of algebraic surfaces (see [8], [3], [5]).

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 6 , 01 December 1989 , pp. 1005 - 1020
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Bese, E., On the spannedness and very ampleness of certain line bundles on the blow-ups of P2 and Fr, Math. Ann. 262(1983), 225–238.Google Scholar
2. Biancofiore, A., On the hyperplane sections of ruled surfaces, Preprint.Google Scholar
3. Biancofiore, A.and Livorni, E. L., On the iteration of the adjunction process in the study of rational surfaces, Ind. Univ. Math. J. 36 (1987), 167–188.Google Scholar
4. Biancofiore, A. On the genus of a hyperplane section of a geometrically ruled surface, Annali di Mat. Pura ed Appl. (IV), 147 (1987), 173–185.Google Scholar
5. Biancofiore, A. On the iteration of the adjunction process for surfaces of negative Kodaira dimension, Manuscripta Math. 64 (1989), 35–54.Google Scholar
6. Bordiga, G., La superficie del 6° ordine con 10 rette nello spazio R4 e le sue proiezioni nello spazio ordinrio, Rom. Ace. L. Mem. 3 (1887), 182–203.Google Scholar
7. Ciliberto, C.and Sernesi, E., Curves on surfaces of degree 2r — δ in Pr , Preprint.Google Scholar
8. Livorni, E. L., On the existence of some surfaces, Preprint.Google Scholar
9. Okonek, C., Moduli reflexiver garben und Flachen vom kleinen Grad in P4, Math.Z. 184 (1983), 549–572.Google Scholar
10. Okonek, C., Uber 2-codimensionale Untermannigfaltigkeiten vom Grad 1 in P4 und P5, Math. Z. 187(1984), 209–219.Google Scholar
11. Okonek, C., Flachen vom Grad 8 in P4, Math. Z. 191 (1986), 207–223.Google Scholar
12. Reider, I., Vector bundles of rank 2 and linear systems on algebraic surfaces, Ann. of Math. 127 (1988), 309–316.Google Scholar
13. Room, T. G., The geometry of determinantal loci (Cambridge University Press, 1938).Google Scholar
14. Sommese, A. J., Hyperplane sections of projective surfaces I. The adjunction mapping, Duke Math. J. 46 (1979), 377–401.Google Scholar
15. Sommese, A.J. and Van de Ven, A., On the adjunction mapping, Math. Ann. 278 (1987), 593– 603.Google Scholar