Complex projective threefolds with non-negative canonical Euler-Poincare characteristic

Details Complex projective threefolds with non-negative canonical Euler-Poincare characteristic Complex projective threefolds with non-negative canonical Euler-Poincare characteristic

2006-09-20

arxiv.org/abs/math/0609545v2

Mathematics

Algebraic Geometry

20 pages, to appear in "Communications in Analysis and Geometry"

Scientific paper

Let $V$ be a complex nonsingular projective 3-fold of general type with
$\chi(\omega_V)\geq 0$ (resp. $>0$). We prove that the m-canonical map
$\Phi_{|mK_V|}$ is birational onto its image for all $m\ge 14$ (resp. $\geq
8$). Known examples show that the lower bound $r_3=14$ (resp. $=8$) is optimal.

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