Gröbner bases and logarithmic D-modules
| Autor: | Castro Jiménez, Francisco Jesús, Ucha Enríquez, José María |
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| Přispěvatelé: | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), Universidad de Sevilla. Departamento de álgebra |
| Rok vydání: | 2006 |
| Předmět: | |
| Zdroj: | idUS. Depósito de Investigación de la Universidad de Sevilla instname |
| Popis: | 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. Ministerio de Ciencia y Tecnología BFM2001-3164 Ministerio de Ciencia y Tecnología MTM2004-01165 Junta de Andalucía FQM-333 |
| Databáze: | OpenAIRE |
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