指数和的IGUSA猜想：非有理奇点的最优估计

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2018-10-26 DOI:10.1017/fmp.2019.3

R. Cluckers, M. Mustaţă, K. Nguyen

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引用次数: 15

摘要

我们证明了满足幂条件的超曲面的对数正则阈值的一个上界，并用它证明了Igusa猜想在指数和上的几个推广，其中对数正则阈值在估计的指数中。通过将对数正则阈值与动力振荡指数的局部概念进行比较，我们证明了这最优地涵盖了非有理奇点猜想的所有情况。

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IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES

We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of the estimates. We show that this covers optimally all situations of the conjectures for nonrational singularities by comparing the log canonical threshold with a local notion of the motivic oscillation index.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464