## Kodai Mathematical Journal

- Kodai Math. J.
- Volume 27, Number 1 (2004), 7-29.

### On threefolds with ${\mathbf K^3=2p_g-6}$

#### Abstract

It is known that if $X$ is an $n$--dimensional normal variety, and $D$ a nef and big Cartier divisor on it such that the associated map $\varphi_D$ is generically finite then $D^n\geq 2(h^0(X,\Oc_X(D))-n)$. We study the case in which the equality holds for $n=3$ and $D=K_X$ is the canonical divisor. \par We also produce a bound for the admissible degree of the canonical map of a threefold, when it is supposed to be generically finite.

#### Article information

**Source**

Kodai Math. J., Volume 27, Number 1 (2004), 7-29.

**Dates**

First available in Project Euclid: 21 May 2004

**Permanent link to this document**

https://projecteuclid.org/euclid.kmj/1085143786

**Digital Object Identifier**

doi:10.2996/kmj/1085143786

**Mathematical Reviews number (MathSciNet)**

MR2042788

**Zentralblatt MATH identifier**

1056.14057

#### Citation

Supino, Paola. On threefolds with ${\mathbf K^3=2p_g-6}$. Kodai Math. J. 27 (2004), no. 1, 7--29. doi:10.2996/kmj/1085143786. https://projecteuclid.org/euclid.kmj/1085143786