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- W3107849682 abstract "We consider the exponent of L ojasiewicz inequality $|partial,f(mathbf z)| ge c |f(mathbf z|^theta$ for two classes of analytic functions and we will give an explicit estimation for $theta$. First we consider certain non-degenerate functions which is not convenient. In S 3.4, we give an example of a polynomial for which $theta_0(f)$ is not constant on the moduli space and in S 3.5, we show that the behaviors of the L ojasiewicz exponents is not similar as the Milnor numbers by an example. In the last section (S 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 L ojasiewicz exponent $theta_0(f)$ using combinatorial data of the Newton boundary of $f$. We generalize this estimation for non-reduced function $g=f_1^{m_1}cdots f_k^{m_k}$." @default.
- W3107849682 created "2020-12-07" @default.
- W3107849682 creator A5058406576 @default.
- W3107849682 date "2020-11-23" @default.
- W3107849682 modified "2023-09-23" @default.
- W3107849682 title "L ojasiewicz exponents of a certain analytic functions" @default.
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- W3107849682 doi "https://doi.org/10.48550/arxiv.2011.11252" @default.
- W3107849682 hasPublicationYear "2020" @default.
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