On canonically derived families of surfaces of general type over curves

Details On canonically derived families of surfaces of general type over curves On canonically derived families of surfaces of general type over curves

2000-03-27

arxiv.org/abs/math/0003173v2

Comm. Algebra 29(2001), no.10, 4597-4618

Mathematics

Algebraic Geometry

19 pages, Amstex, Accepted for publication in Communications in Algebra

Scientific paper

Suppose X is a smooth projective 3-fold of general type and |mK_X| is composed of a pencil of surfaces with m>1. This pencil naturally induces a fibration f:X->C onto a smooth curve C after the Stein-factorization, which is the main objects of this article. Based on Koll'ar's earlier works, we improve on it and try to understand the family in terms of discrete birational invariants of the total space as well as those of the general fiber and the base curve. The aim of this note is to build a little bit basic facts.

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