On minimal 3-folds of general type with maximal pluricanonical section index

Meng Chen

On minimal 3-folds of general type with maximal pluricanonical section index

Algebraic Geometry 2017-06-06 v2

Authors: Meng Chen

Abstract

Let $X$ be a minimal projective 3-fold of general type. The pluricanonical section index $\delta(X)$ is defined to be the minimal integer $m$ so that $P_{m}(X)\geq 2$ . According to Chen-Chen, one has either $1\leq \delta(X)\leq 15$ or $\delta(X)=18$ . This note aims to intensively study those with maximal such index. A direct corollary is that the $57$ th canonical map of every minimal 3-fold of general type is stably birational.

Keywords

minimal 3-folds general type pluricanonical section index canonical map birational geometry algebraic geometry

Cite

@article{arxiv.1604.04828,
  title  = {On minimal 3-folds of general type with maximal pluricanonical section index},
  author = {Meng Chen},
  journal= {arXiv preprint arXiv:1604.04828},
  year   = {2017}
}

Comments

To appear in The Asian Journal of Mathematics (Special issue for Ngaiming Mok's sixtieth birthday)

On minimal 3-folds of general type with maximal pluricanonical section index

Abstract

Keywords

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