| Autor: |
Puthenpurakal, Tony J., Sahoo, Samarendra |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Let $(A,\mathfrak{m})$ be an analytically un-ramified Noetherian local ring of dimension $d \geq 1$, $I$ a regular $\mathfrak{m}$-primary ideal of $A$ and let $\overline{I}$ be integral closure ideal of $I$. If $A$ is of characteristic $p > 0$ then let $I^*$ denote the tight closure of $I$. Let $G_I(A)=\bigoplus_{n\geq 0}I^n/I^{n+1}$ be the associated graded ring of $A$ with respect to $I$. Assume $G_I(A)$ is unmixed and equi-dimensional. We show that either the function $P_{\overline{I}} :\,n\mapsto \lambda(\overline{I^n}/I^n)$ is a polynomial type of degree $d-1$ or $\overline{I^n}=I^n$ for all $n\geq 1.$ We prove an analogus result for the tight closure filtration if $A$ is of characteristic $p > 0$. When $A$ is generalized Cohen-Macaulay and $I$ is generated by standard system of parameters we give bounds for the first Hilbert coefficients of the integral closure filtration of $I$ and the tight closure filtration of $I$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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