## Journal of the Mathematical Society of Japan

### Varieties of small degree with respect to codimension and ample vector bundles

#### Abstract

Let  $\mathscr{E}$  be an ample vector bundle on a projective manifold $X$, with a section vanishing on a smooth subvariety $Z$  of the expected dimension, and let $H$  be an ample line bundle on $X$  inducing a very ample ample line bundle $H_Z$  on $Z$. Triplets $(X, \mathscr{E}, H)$ as above are classified assuming that $Z$, embedded by $|H_Z|$, is a variety of small degree with respect to codimension.

#### Article information

Source
J. Math. Soc. Japan, Volume 60, Number 2 (2008), 341-361.

Dates
First available in Project Euclid: 30 May 2008

https://projecteuclid.org/euclid.jmsj/1212156654

Digital Object Identifier
doi:10.2969/jmsj/06020341

Mathematical Reviews number (MathSciNet)
MR2421980

Zentralblatt MATH identifier
1170.14030

#### Citation

LANTERI, Antonio; NOVELLI, Carla. Varieties of small degree with respect to codimension and ample vector bundles. J. Math. Soc. Japan 60 (2008), no. 2, 341--361. doi:10.2969/jmsj/06020341. https://projecteuclid.org/euclid.jmsj/1212156654

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