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April, 1999 Complex varieties of general type whose canonical systems are composed with pencils
Meng CHEN
J. Math. Soc. Japan 51(2): 331-335 (April, 1999). DOI: 10.2969/jmsj/05120331

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.

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Meng CHEN. "Complex varieties of general type whose canonical systems are composed with pencils." J. Math. Soc. Japan 51 (2) 331 - 335, April, 1999. https://doi.org/10.2969/jmsj/05120331

Information

Published: April, 1999
First available in Project Euclid: 10 June 2008

zbMATH: 0927.14003
MathSciNet: MR1674752
Digital Object Identifier: 10.2969/jmsj/05120331

Subjects:
Primary: 14C20 , 14E35
Secondary: 14J10

Keywords: Canonical pencil , fibration , vector bundles

Rights: Copyright © 1999 Mathematical Society of Japan

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Vol.51 • No. 2 • April, 1999
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