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摘要翻译：
设T_n表示对(X，Y)的对数规范门限集，其中X是维数n的非奇异变化，Y是X的非空闭子格式。利用非标准方法，我们证明了T_n中递减序列的每一极限都位于T_{n-1}中，并在此条件下证明了Koll{a}R的一个猜想。我们还证明了T_n是实数集合中的闭子集；特别地，固定维数光滑变种上的对数规范阈值的每一个极限都是有理数。作为这个性质的结果，我们看到，为了检验所有T_n的Shokurov ACC猜想，只要证明1不是任何T_n下面的累加点就足够了。在不同的方向上，我们将ACC猜想解释为形式幂级数对数正则阈值的半连续性质。
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英文标题：
《Limits of log canonical thresholds》
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作者：
Tommaso de Fernex and Mircea Mustata
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let T_n denote the set of log canonical thresholds of pairs (X,Y), with X a nonsingular variety of dimension n, and Y a nonempty closed subscheme of X. Using non-standard methods, we show that every limit of a decreasing sequence in T_n lies in T_{n-1}, proving in this setting a conjecture of Koll\'{a}r. We also show that T_n is a closed subset in the set of real numbers; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in order to check Shokurov's ACC Conjecture for all T_n, it is enough to show that 1 is not a point of accumulation from below of any T_n. In a different direction, we interpret the ACC Conjecture as a semi-continuity property for log canonical thresholds of formal power series.
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PDF链接：
https://arxiv.org/pdf/0710.4978
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