The log canonical threshold of products of ideals and mixed Łojasiewicz exponents
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912039898710016 |
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| author | Bivià-Ausina, Carles |
| author_facet | Bivià-Ausina, Carles |
| contents | Given two ideals $I$ and $J$ of the ring $\mathcal O_n$ of analytic function germs $f:(\mathbb C^n,0)\to \mathbb C$, we show a sharp lower bound for the log canonical threshold of $IJ$ in terms of the sequences of mixed Łojasiewicz exponents of them. In particular, in the case where $J$ is the maximal ideal, the corresponding equality holds if and only if the integral closure of $I$ equals some power of the maximal ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14251 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The log canonical threshold of products of ideals and mixed Łojasiewicz exponents Bivià-Ausina, Carles Commutative Algebra Algebraic Geometry Complex Variables 32S05 Given two ideals $I$ and $J$ of the ring $\mathcal O_n$ of analytic function germs $f:(\mathbb C^n,0)\to \mathbb C$, we show a sharp lower bound for the log canonical threshold of $IJ$ in terms of the sequences of mixed Łojasiewicz exponents of them. In particular, in the case where $J$ is the maximal ideal, the corresponding equality holds if and only if the integral closure of $I$ equals some power of the maximal ideal. |
| title | The log canonical threshold of products of ideals and mixed Łojasiewicz exponents |
| topic | Commutative Algebra Algebraic Geometry Complex Variables 32S05 |
| url | https://arxiv.org/abs/2409.14251 |