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

Meng Chen; Kang Zuo

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

Algebraic Geometry 2007-10-23 v2

Authors: Meng Chen , Kang Zuo

Abstract

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.

Keywords

manifolds nef and ample line bundles

Cite

@article{arxiv.math/0609545,
  title  = {Complex projective threefolds with non-negative canonical Euler-Poincare characteristic},
  author = {Meng Chen and Kang Zuo},
  journal= {arXiv preprint arXiv:math/0609545},
  year   = {2007}
}

Comments

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

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