Let E be an ample vector bundle of rank r \geq 2 on a smooth complex projective n-fold X having a section whose zero locus, Z, is a smooth submanifold of the expected dimension n-r \geq 3. Pairs (X,E) as above are classified in the following cases: a) Z is a projective bundle over a smooth curve of positive genus, b) (Z,H_Z) is a scroll over a smooth curve B, and c) (Z,H_Z) is a quadric fibration over B, for some ample nine bundle H on X.

Ample vector bundle characterizations of projective bundles and quadric fibrations over curves / A. Lanteri, H. Maeda - In: Higher dimensional complex varieties / [a cura di] M. Andreatta, Th. Peternell. - Berlin : Walter de Gruyter, 1996. - pp. 247-259

### Ample vector bundle characterizations of projective bundles and quadric fibrations over curves

#### Abstract

Let E be an ample vector bundle of rank r \geq 2 on a smooth complex projective n-fold X having a section whose zero locus, Z, is a smooth submanifold of the expected dimension n-r \geq 3. Pairs (X,E) as above are classified in the following cases: a) Z is a projective bundle over a smooth curve of positive genus, b) (Z,H_Z) is a scroll over a smooth curve B, and c) (Z,H_Z) is a quadric fibration over B, for some ample nine bundle H on X.
##### Scheda breve Scheda completa Scheda completa (DC)
ammple vector bundle; projective bundle, scroll, quadric fibration
Settore MAT/03 - Geometria
Book Part (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
##### Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/2434/185559`
• ND
• ND
• ND