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arXiv · 1708.02278

Optimal bounds for T-singularities in stable surfaces

Julie Rana·Giancarlo Urzúa
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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.

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Julie Rana, Giancarlo Urzúa. 2017-08-07. Optimal bounds for T-singularities in stable surfaces. https://arxiv.org/abs/1708.02278

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