Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 51, Number 2 (1999), 331-335.
Complex varieties of general type whose canonical systems are composed with pencils
This paper aims to study a variety of general type whose canonical system is composed with a pencil. This kind of variety admits a natural fibration onto a nonsingular curve. A natural problem is whether the geometric genus of the general fiber of this fibration is bounded. A simple classification is given in this paper. When the object is a nonsingular minimal 3-fold of general type, if the canonical system is composed of an irrational pencil, then the geometric genus of the general fibre is bounded. If the canonical system is composed of a rational pencil, it seems that the geometric genus of the general fibre is not bounded though no counter examples have been found.
J. Math. Soc. Japan, Volume 51, Number 2 (1999), 331-335.
First available in Project Euclid: 10 June 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14C20: Divisors, linear systems, invertible sheaves 14E35
Secondary: 14J10: Families, moduli, classification: algebraic theory
CHEN, Meng. Complex varieties of general type whose canonical systems are composed with pencils. J. Math. Soc. Japan 51 (1999), no. 2, 331--335. doi:10.2969/jmsj/05120331. https://projecteuclid.org/euclid.jmsj/1213108020