Integral closure and bounds for quotients of multiplicities of monomial ideals
[EN] Given a pair of monomial ideals $I$ and $J$ of finite colength of the ring of analytic function germs $(\C^n,0)\to \C$, we prove that some power of $I$ admits a reduction formed by homogeneous polynomials with respect to the Newton filtration induced by $J$ if and only if the quotient of multip...
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| Format: | article |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/103293 |
| Online Access: | https://riunet.upv.es/handle/10251/103293 |
| Access Level: | Open access |
| Keyword: | Integral closure of ideals Mixed multiplicities of ideals Monomial ideals Newton polyhedra MATEMATICA APLICADA |
| Summary: | [EN] Given a pair of monomial ideals $I$ and $J$ of finite colength of the ring of analytic function germs $(\C^n,0)\to \C$, we prove that some power of $I$ admits a reduction formed by homogeneous polynomials with respect to the Newton filtration induced by $J$ if and only if the quotient of multiplicities $e(I)/e(J)$ attains a suitable upper bound expressed in terms of the Newton polyhedra of $I$ and $J$. We also explore other connections between mixed multiplicities, Newton filtrations and the integral closure of ideals. |
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