Sunto
SiaX una superficie complessa compatta non singolare senza funzioni meromorfe non costanti. In questo lavoro si domstra cheX possiede molti fibrati olomorfi di rango 2 contenenti un unico fibrato in rette.
Abstract
LetX be a smooth complex compact surface without non-constant meromorphic functions. Here we prove the existence of rank holomorphic vector bundles onX containing exactly one rank one saturated subsheaf.
References
[BL]C. Banica—J. Le Potier,Ssur l’existence des fibrés vectoriels holomorphes sur les surfaces non-algébriques, J. reine angw. Math.,378 (1987), pp. 121–143.
[BPV]W. Barth—C. Peters—A. Van de Ven,Compact Complex Surfaces, Ergebnisse der Math. 3. Folge-Band 4, Springer-Verlag, 1984.
[B]V. Brinzanescu,Holomorphic Vector Bundles over Compact Complex Surfaces, Lect. Notes in Math. 1624, Springer, 1996.
[C]F. Catanese,Footnotes to a theorem of I. Reider, in: Algebraic Geometry, Proceedings L’Aquila 1988, pp. 67–74 Lect. Notes in Math. 1417, Springer, 1990.
[U]K. Ueno,Classification theory of algebraic varieties and compact complex spaces, Lect. Notes in Math. 439, Springer, Heidelberg, 1975