## Journal of the Mathematical Society of Japan

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

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

Gian Mario BESANA and Sandra Dl ROCCO

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.2969/jmsj/05420329

**Mathematical Reviews number (MathSciNet)**

MR1883521

**Zentralblatt MATH identifier**

1056.14009

**Subjects**

Primary: 14N30: Adjunction problems 14J99: None of the above, but in this section

Secondary: 14J25: Special surfaces {For Hilbert modular surfaces, see 14G35}

**Keywords**

Polarized surfaces adjunction theory

#### 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