论文标题
某些分析功能的oljasiewicz指数
Łojasiewicz exponents of a certain analytic functions
论文作者
论文摘要
我们考虑了lojasiewicz不平等的指数$ \ | \ partial \，f（\ mathbf z）\ | \ ge c | f（\ Mathbf z |^θ$用于两类分析功能，我们将对$θ$进行明确的估计。首先，我们考虑某些不方便的非脱位函数。在第3.4节中，我们给出了一个$θ_0（f）$ noction and the Moduli和Moduli and the Moduli and prasti and of the prasti and presti and presti and of the presti and。以示例为示例，oljasiewicz指数与Milnor数字不同。 在最后一节（第4节）中，我们还给出了产品功能的估计$ f（\ mathbf z）= f_1（\ mathbf z）\ cdots f_k（\ mathbf z）$ f_k（\ mathbf z）$与特定方便的非替代性非分类的家庭相关的家族相关。在这两个类别中，奇异性都不是孤立的。我们将使用$ f $的牛顿边界的组合数据对lojasiewicz指数$θ_0（f）$进行明确估计。我们对非还原函数的此估计概括$ g = f_1^{m_1} \ cdots f_k^{m_k} $。
We consider the exponent of Łojasiewicz inequality $\|\partial\,f(\mathbf z)\| \ge c |f(\mathbf z|^θ$ for two classes of analytic functions and we will give an explicit estimation for $θ$. First we consider certain non-degenerate functions which is not convenient. In §3.4, we give an example of a polynomial for which $θ_0(f)$ is not constant on the moduli space and in §3.5, we show that the behaviors of the Łojasiewicz exponents is not similar as the Milnor numbers by an example. In the last section (§4), we give also an estimation for product functions $f(\mathbf z)=f_1(\mathbf z)\cdots f_k(\mathbf z)$ associated to a family of a certain convenient non-degenerate complete intersection varieties. In either class, the singularity is not isolated. We will give explicit estimations of the Łojasiewicz exponent $θ_0(f)$ using combinatorial data of the Newton boundary of $f$. We generalize this estimation for non-reduced function $g=f_1^{m_1}\cdots f_k^{m_k}$.
