Kodai Mathematical Journal

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

Paola Supino

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

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