Canonical stability of 3-folds of general type with p_g≥ 3

2002/11/30 by Meng Chen
Mathematics · #math.AG

paper · pdf

published as International Journal of Math. 14(2003), 515-528 · Latex 14 pages, the final version, to appear in International Journal of Mathematics

arxiv created 2003/05/16 · arxiv updated 2009/11/30

Abstract

We study the canonical stability of a smooth projective 3-fold V of general type. We prove that (1) |5K_V| gives a birational map onto its image provided the geometric genus p_g≥ 4; (2) |6K_V| gives a birational map provided p_g=3. Known examples show that both are optimal. This fact can be viewed as parallel to surface case, though people know very little on 3-folds of general type with p_g≤ 1.

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