## Journal of the Mathematical Society of Japan

### On polarized surfaces of low degree whose adjoint bundles are not spanned

#### Abstract

Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to be the only examples in degree three. Two classes of examples in degree four are presented, one of which is shown to characterize regular such pairs. A Reider-type theorem is obtained in which the assumption on the degree of $L$ is removed.

#### Article information

Source
J. Math. Soc. Japan, Volume 54, Number 2 (2002), 329-340.

Dates
First available in Project Euclid: 9 June 2008

https://projecteuclid.org/euclid.jmsj/1213024070

Digital Object Identifier
doi:10.2969/jmsj/05420329

Mathematical Reviews number (MathSciNet)
MR1883521

Zentralblatt MATH identifier
1056.14009

#### Citation

BESANA, Gian Mario; Dl ROCCO, Sandra. On polarized surfaces of low degree whose adjoint bundles are not spanned. J. Math. Soc. Japan 54 (2002), no. 2, 329--340. doi:10.2969/jmsj/05420329. https://projecteuclid.org/euclid.jmsj/1213024070