Valuation spaces and multiplier ideals on singular varieties
Valuation spaces and multiplier ideals on singular varieties
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单一品种的估值空间和乘数理想
DOI：
10.1007/9781107416000.004
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Urbinati
中科院分区：
文献类型：
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作者：
S. Boucksom;T. Fernex;C. Favre;S. Urbinati
我们将光滑情况下由Boucksom-Favre-Jonsson引起的乘子理想的赋值表征推广到所有正规复代数变数。为此，我们将对数差异函数扩展到所有实值的空间，并在Jonsson-Mustaţă先前工作的基础上证明它满足充分的性质。接下来，我们给出了前三位作者所引入的数值卡地亚除数概念的另一种定义，并证明了对于有理性奇点，数值q -卡地亚除数与q -卡地亚除数重合。这些想法自然导致了数值上的Q-Gorenstein变量的概念，我们对乘数理想的价值表征采用了一种特别简单的形式。
We generalize to all normal complex algebraic varieties the valuative characterization of multiplier ideals due to Boucksom-Favre-Jonsson in the smooth case. To that end, we extend the log discrepancy function to the space of all real valuations, and prove that it satisfies an adequate properness property, building upon previous work by Jonsson-Mustaţă. We next give an alternative definition of the concept of numerically Cartier divisors previously introduced by the first three authors, and prove that numerically Q-Cartier divisors coincide with Q-Cartier divisors for rational singularities. These ideas naturally lead to the notion of numerically Q-Gorenstein varieties, for which our valuative characterization of multiplier ideals takes a particularly simple form.