Rational powers, invariant ideals, and the summation formula
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915230224744448 |
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| author | Bisui, Sankhaneel Das, Sudipta Hà, Tài Huy Montaño, Jonathan |
| author_facet | Bisui, Sankhaneel Das, Sudipta Hà, Tài Huy Montaño, Jonathan |
| contents | We provide explicit descriptions for the rational powers and Rees valuations of several classes of ideals invariant under natural actions of tori and products of general linear groups, in terms of polyhedra and lattice points. This allows us to show that a version of Mustaţă-Takagi's summation formula for multiplier ideals also holds for the rational powers of these ideals. Moreover, for arbitrary ideals in normal domains that are finitely generated over algebraically closed fields, we prove a weaker version of this formula that holds for sufficiently large rational numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational powers, invariant ideals, and the summation formula Bisui, Sankhaneel Das, Sudipta Hà, Tài Huy Montaño, Jonathan Commutative Algebra We provide explicit descriptions for the rational powers and Rees valuations of several classes of ideals invariant under natural actions of tori and products of general linear groups, in terms of polyhedra and lattice points. This allows us to show that a version of Mustaţă-Takagi's summation formula for multiplier ideals also holds for the rational powers of these ideals. Moreover, for arbitrary ideals in normal domains that are finitely generated over algebraically closed fields, we prove a weaker version of this formula that holds for sufficiently large rational numbers. |
| title | Rational powers, invariant ideals, and the summation formula |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2402.12350 |