Canonical stability of 3-folds of general type with $p_g\geq 3$

Details Canonical stability of 3-folds of general type with $p_g\geq 3$ Canonical stability of 3-folds of general type with $p_g\geq 3$

2002-11-16

arxiv.org/abs/math/0211251v5

International Journal of Math. 14(2003), 515-528

Mathematics

Algebraic Geometry

Latex 14 pages, the final version, to appear in International Journal of Mathematics

Scientific paper

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 $p_g\geq 4$; (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 $p_g\leq 1$.

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