对数 Calabi-Yau 三折的互补有界性

arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-02 DOI:arxiv-2409.01310

Guodu Chen, Jingjun Han, Qingyuan Xue

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引用次数: 0

摘要

在本文中，我们研究了肖库罗夫（Shokurov）为系数集$[0,1]$的卡拉比-尤（Calabi-Yau）型变体引入的补集理论。我们证明了存在一个有限的正整数集 $\mathcal{N}$，使得如果三折对 $(X/Z\ni z,B)$ 有一个 $\mathbb{R}$ 的补集，而这个补集在 $z$ 的邻域上是 klt，那么对于某个 $n\in\mathcal{N}$，它就有一个 $n$ 的补集。我们还证明了$mathbb{R}$互补曲面对的互补有界性。

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Boundedness of complements for log Calabi-Yau threefolds

In this paper, we study the theory of complements, introduced by Shokurov, for Calabi-Yau type varieties with the coefficient set $[0,1]$. We show that there exists a finite set of positive integers $\mathcal{N}$, such that if a threefold pair $(X/Z\ni z,B)$ has an $\mathbb{R}$-complement which is klt over a neighborhood of $z$, then it has an $n$-complement for some $n\in\mathcal{N}$. We also show the boundedness of complements for $\mathbb{R}$-complementary surface pairs.

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arXiv - MATH - Algebraic Geometry

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