Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T02:08:23.591Z Has data issue: false hasContentIssue false
  • English
  • Français

WEAKLY UNIFORM RANK TWO VECTOR BUNDLES ON MULTIPROJECTIVE SPACES

Part of: (Co)homology theory

Published online by Cambridge University Press:  21 July 2011

EDOARDO BALLICO  and
FRANCESCO MALASPINA
EDOARDO BALLICO
Affiliation:
Università di Trento, 38123 Povo (TN), Italy (email: [email protected])
FRANCESCO MALASPINA*
Affiliation:
Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Here we classify the weakly uniform rank two vector bundles on multiprojective spaces. Moreover, we show that every rank r>2 weakly uniform vector bundle with splitting type a1,1=⋯=ar,s=0 is trivial and every rank r>2 uniform vector bundle with splitting type a1>⋯>ar splits.

Keywords

uniform vector bundlessplitting typemultiprojective spaces

MSC classification

Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 255 - 260
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Ballico, E. and Ellia, P., ‘Fibrés uniformes de rang 5 sur ℙ3’, Bull. Soc. Math. France 111 (1983), 59–87.CrossRefGoogle Scholar
[2]Ballico, E. and Newstead, P. E., ‘Uniform bundles on quadric surfaces and some related varieties’, J. Lond. Math. Soc. (2) 31(2) (1985), 211–223.CrossRefGoogle Scholar
[3]Drezet, J. M., ‘Exemples de fibres uniformes nonhomogènes sur Pn’, C. R. Acad. Sci. Paris Sér. A 291 (1980), 125–128.Google Scholar
[4]Elencwajg, G., ‘Les fibrés uniformes de rang 3 sur P2(C) sont homegènes’, Math. Ann. 231 (1978), 217–227.CrossRefGoogle Scholar
[5]Elencwajg, G., Hirschowitz, A. and Schneider, M., ‘Les fibres uniformes de rang au plus n sur Pn(C) sont ceux qu’on croit’, in: Vector Bundles and Differential Equations (Proc. Conf., Nice, 1979), Progress in Mathematics, 7 (Birkhäuser, Boston, MA, 1980), pp. 37–63.CrossRefGoogle Scholar
[6]Ellia, P., ‘Sur les fibrés uniformes de rang (n+1) sur ℙn’, Mém. Soc. Math. Fr. 7 (1982), 59–87.Google Scholar
[7]Newstead, P. E. and Schwarzenberger, R. L. E., ‘Reducible vector bundles on a quadric surface’, Proc. Cambridge Philos. Soc. 60 (1964), 421–424.CrossRefGoogle Scholar
[8]Okonek, Ch., Schneider, M. and Spindler, H., Vector Bundles on Complex Projective Spaces, Progress in Mathematics, 3 (Birkhäuser, Boston, MA, 1980).Google Scholar
[9]Sato, E., ‘Uniform vector bundles on a projective space’, J. Math. Soc. Japan 28 (1976), 123–132.CrossRefGoogle Scholar
[10]Schwarzenberger, R. L. E., ‘Reducible vector bundles on a quadric surface’, Proc. Cambridge Philos. Soc. 58 (1962), 209–216.CrossRefGoogle Scholar
[11]Van de Ven, A., ‘On uniform vector bundles’, Math. Ann. 195 (1972), 245–248.CrossRefGoogle Scholar