Optimal bounds for T-singularities in stable surfaces

Julie Rana; Giancarlo Urzúa

Optimal bounds for T-singularities in stable surfaces

Algebraic Geometry 2020-01-28 v2

Authors: Julie Rana , Giancarlo Urzúa

Abstract

We explicitly bound T-singularities on normal projective surfaces $W$ with one singularity, and $K_W$ ample. This bound depends only on $K_W^2$ , and it is optimal when $W$ is not rational. We classify and realize surfaces attaining the bound for each Kodaira dimension of the minimal resolution of $W$ . This answers effectiveness of bounds (see [Alexeev94], [Alexeev-Mori04], [Lee99]) for those surfaces.

Keywords

singularity theory del pezzo surfaces algebraic surfaces

Cite

@article{arxiv.1708.02278,
  title  = {Optimal bounds for T-singularities in stable surfaces},
  author = {Julie Rana and Giancarlo Urzúa},
  journal= {arXiv preprint arXiv:1708.02278},
  year   = {2020}
}

Comments

We corrected a minor error in the proof of Theorem 3.2(A). With this, the classification in Theorem 3.2 (when the Kodaira dimension 1 bound is optimal) adds four more cases

Optimal bounds for T-singularities in stable surfaces

Abstract

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