Existence of minimal models for threefold generalized pairs in positive characteristic

Fuente: arXiv
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Main Authors: Yang, Tianle, Ye, Zelin, Zhang, Zhiyao
Format: Preprint
Published: 2024
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author Yang, Tianle
Ye, Zelin
Zhang, Zhiyao
author_facet Yang, Tianle
Ye, Zelin
Zhang, Zhiyao
contents Let $\mathbb{K}$ be an algebraically closed field of characteristic $p>5$. We show the existence of minimal models for pseudo-effective NQC lc generalized pairs in dimension three over $\mathbb{K}$. As a consequence, we prove the termination of flips for pseudo-effective threefold NQC lc generalized pairs over $\mathbb{K}$. This provides a new proof on the termination of flips for pseudo-effective pairs over $\mathbb{K}$ without using the non-vanishing theorems. A key ingredient of our proof is the ACC for lc thresholds in dimension $\leq 3$ and the global ACC in dimension $\leq 2$ for generalized pairs over $\mathbb{K}$.
format Preprint
id arxiv_https___arxiv_org_abs_2408_12269
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Existence of minimal models for threefold generalized pairs in positive characteristic
Yang, Tianle
Ye, Zelin
Zhang, Zhiyao
Algebraic Geometry
14E30, 14B05
Let $\mathbb{K}$ be an algebraically closed field of characteristic $p>5$. We show the existence of minimal models for pseudo-effective NQC lc generalized pairs in dimension three over $\mathbb{K}$. As a consequence, we prove the termination of flips for pseudo-effective threefold NQC lc generalized pairs over $\mathbb{K}$. This provides a new proof on the termination of flips for pseudo-effective pairs over $\mathbb{K}$ without using the non-vanishing theorems. A key ingredient of our proof is the ACC for lc thresholds in dimension $\leq 3$ and the global ACC in dimension $\leq 2$ for generalized pairs over $\mathbb{K}$.
title Existence of minimal models for threefold generalized pairs in positive characteristic
topic Algebraic Geometry
14E30, 14B05
url https://arxiv.org/abs/2408.12269