Journal of the Mathematical Society of Japan

Complex varieties of general type whose canonical systems are composed with pencils

Meng CHEN

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 2 (1999), 331-335.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213108020

Digital Object Identifier
doi:10.2969/jmsj/05120331

Mathematical Reviews number (MathSciNet)
MR1674752

Zentralblatt MATH identifier
0927.14003

Subjects
Primary: 14C20: Divisors, linear systems, invertible sheaves 14E35
Secondary: 14J10: Families, moduli, classification: algebraic theory

Keywords
Canonical pencil fibration vector bundles

Citation

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


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