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
A. LanteriPrimo
;
1996
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.Pubblicazioni consigliate
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