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Irregularity of canonical pencils for a threefold of general type

Published online by Cambridge University Press:  01 January 1999

MENG CHEN  and
ZHIJIE J. CHEN
MENG CHEN
Affiliation:
Department of Applied Mathematics, Tongji University, Shanghai, 200092 China
ZHIJIE J. CHEN
Affiliation:
Department of Mathematics, East China Normal University, Shanghai, 200062 China
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Abstract

Let X be a complex nonsingular projective threefold of general type. Suppose the canonical system of X is composed of a pencil, i.e. dimΦ∼KX∼(X)=1. It is often important to understand birational invariants of X such as pg(X), q(X), h2(OX) and χ(OX) etc. In this paper, we mainly study the irregularity of X.

We may suppose that ∼KX∼ is free of base points. There is a natural fibration f[ratio ]X→C onto a nonsingular curve after the Stein factorization of Φ∼KX∼. Let F be a general fibre of f, then we know that F is a nonsingular projective surface of general type. Set b[ratio ]=g(C) and pg(F), q(F) for the respective invariants of F. The main result is the following theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 125 , Issue 1 , January 1999 , pp. 83 - 87
Copyright
Cambridge Philosophical Society 1999

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Footnotes

Project partially supported by NNSFC.