Bounds for degrees of syzygies of polynomials defining a grade two ideal
We make explicit the exponential bound on the degrees of the polynomials appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with the Hilbert-Burch Theorem to show that the syzygy module of a sequence of $m$ polynomials in $n$ variables defining a complete intersection ideal of g...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/196304 |
| Acceso en línea: | https://hdl.handle.net/2445/196304 |
| Access Level: | acceso abierto |
| Palabra clave: | Àlgebra commutativa Àlgebra homològica Anells commutatius Geometria algebraica Algorismes computacionals Commutative algebra Homological algebra Commutative rings Algebraic geometry Computer algorithms |
| Sumario: | We make explicit the exponential bound on the degrees of the polynomials appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with the Hilbert-Burch Theorem to show that the syzygy module of a sequence of $m$ polynomials in $n$ variables defining a complete intersection ideal of grade two is free, and that a basis of it can be computed with bounded degrees. In the known cases, these bounds improve previous results. |
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