Gröbner bases and logarithmic D-modules
Let C[x] = C[x1, . . . , xn] be the ring of polynomials with complex coefficients and An the Weyl algebra of order n over C. Elements in An are linear differential operators with polynomial coefficients. For each polynomial f , the ring M = C[x] f of rational functions with poles along f has a natur...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2006 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/93582 |
| Acesso em linha: | https://hdl.handle.net/11441/93582 https://doi.org/10.1016/j.jsc.2004.04.011 |
| Access Level: | acceso abierto |
| Palavra-chave: | Gröbner bases Weyl algebra D-Modules Free divisors Spencer divisors |
| Resumo: | Let C[x] = C[x1, . . . , xn] be the ring of polynomials with complex coefficients and An the Weyl algebra of order n over C. Elements in An are linear differential operators with polynomial coefficients. For each polynomial f , the ring M = C[x] f of rational functions with poles along f has a natural structure of a left An-module which is finitely generated by a classical result of I.N. Bernstein. A central problem in this context is how to find a finite presentation of M starting from the input f . In this paper we use Gr¨obner base theory in the non-commutative frame of the ring An to compare M to some other An-modules arising in Singularity Theory as the so-called logarithmic An-modules. We also show how the analytic case can be treated with computations in the Weyl algebra if the input data f is a polynomial. |
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