Finite determination conjecture for Mather–Jacobian minimal log discrepancies and its applications
Finite determination conjecture for Mather–Jacobian minimal log discrepancies and its applications
复制标题
Mather-Jacobian最小对数差异的有限判定猜想及其应用
DOI：
10.1007/s40879-018-0217-1
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发表时间：
2017
影响因子：
0.6
通讯作者：
S. Ishii
中科院分区：
文献类型：
--
作者：
S. Ishii
研究了任意特征的奇点。本文利用奇异喷流格式提出了Mather-Jacobian最小对数偏差的有限决定性猜想。该猜想等价于爆破次数的有界性，从而得到一个计算Mather-Jacobian最小对数偏差的素因子。我们还表明，这一猜想产生了一些基本性质的奇点，例如，Mather-Jacobian（log）正则奇点的开放性，这些奇点在小变形下的稳定性和Mather-Jacobian最小对数偏差的下半连续性，这些特征在特征0和正特征情况下是已知的。例如，对于特征不为2的任意维非退化超曲面和特征不为2的2维奇点，我们给出了猜想的一些证据。我们还给出了一个界的爆破次数，以获得一个素因子，计算的Mather-Jacobian最小对数偏差。
We study singularities in arbitrary characteristic. We propose finite determination conjecture for Mather–Jacobian minimal log discrepancies in terms of jet schemes of a singularity. The conjecture is equivalent to the boundedness of the number of the blow-ups to obtain a prime divisor which computes the Mather–Jacobian minimal log discrepancy. We also show that this conjecture yields some basic properties of singularities; e.g., openness of Mather–Jacobian (log) canonical singularities, stability of these singularities under small deformations and lower semi-continuity of Mather–Jacobian minimal log discrepancies, which are already known in characteristic 0 and open for positive characteristic case. We show some evidences of the conjecture: for example, for non-degenerate hypersurface of any dimension in arbitrary characteristic and 2-dimensional singularities in characteristic not 2. We also give a bound of the number of the blow-ups to obtain a prime divisor which computes the Mather–Jacobian minimal log discrepancy.
射流方案的几何特性
DOI：
--
发表时间：
2011
期刊：
Comm.in Alg. in press
影响因子：
--
作者：
H.Akiyoshi;H.sakuma;H.woda;Y.Yamashita;S.Ishii
通讯作者：
S.Ishii
喷射方案、弧空间和纳什问题
DOI：
--
发表时间：
2007
期刊：
C.R.Math.Rep.Acad.Canada 29
影响因子：
--
作者：
M. Jimbo;K. Momihara;S. Yoshikawa;S.Ishii
通讯作者：
S.Ishii