On minimal 3-folds with $K^3\geq 86$

Meng Chen; Sicheng Ding

On minimal 3-folds with $K^3\geq 86$

Algebraic Geometry 2025-10-07 v1

Authors: Meng Chen , Sicheng Ding

Abstract

We prove that the $5$ -canonical map of every minimal projective $3$ -fold $X$ with $K_X^3\geq 86$ is stably birational onto its image, which loosens previous requirements $K_X^3>4355^3$ and $K_X^3>12^3$ respectively given by Todorov and Chen. The essential technical ingredient of this paper is an efficient utilization of a moving divisor which grows from global $2$ -forms by virtue of Chen-Jiang.

Keywords

minimal 3-folds 5-canonical map stable birational K^3 Chen-Jiang

Cite

@article{arxiv.2510.04029,
  title  = {On minimal 3-folds with $K^3\geq 86$},
  author = {Meng Chen and Sicheng Ding},
  journal= {arXiv preprint arXiv:2510.04029},
  year   = {2025}
}

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