论文标题
ACC用于本地卷和奇点的界限
ACC for local volumes and boundedness of singularities
论文作者
论文摘要
局部体积的ACC猜想预测，如果$δ$的系数属于DCC集合，则（x，δ）$ in（x，δ）$ x \ in（x，δ）$的局部卷集满足了ACC。在本文中，我们证明了局部体积的ACC猜想，假设环境细菌是分析界限的。我们介绍了另一个相关的猜想，该猜想预测了KLT奇点的$δ$ -PLT爆炸的存在，其局部体积的下限为正。我们表明，当环境细菌分析界限时，后一种猜想也存在。此外，我们证明这两种猜想都在维度2以及三维终端奇点中。
The ACC conjecture for local volumes predicts that the set of local volumes of klt singularities $x\in (X,Δ)$ satisfies the ACC if the coefficients of $Δ$ belong to a DCC set. In this paper, we prove the ACC conjecture for local volumes under the assumption that the ambient germ is analytically bounded. We introduce another related conjecture, which predicts the existence of $δ$-plt blow-ups of a klt singularity whose local volume has a positive lower bound. We show that the latter conjecture also holds when the ambient germ is analytically bounded. Moreover, we prove that both conjectures hold in dimension 2 as well as for 3-dimensional terminal singularities.
