Artículo
A vanishing theorem for a class of logarithmic D-modules
Autor/es | Castro Jiménez, Francisco Jesús
Gago Vargas, J. Hartillo Hermoso, Isabel Ucha Enríquez, José María |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Álgebra |
Fecha de publicación | 2007 |
Fecha de depósito | 2020-02-18 |
Publicado en |
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Resumen | Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the
sheaf of linear differential operators with holomorphic coefficients) on X =
Cn. Let D X be a locally weakly quasi-homogeneous free divisor defined
by ... Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on X = Cn. Let D X be a locally weakly quasi-homogeneous free divisor defined by a polynomial f. In this paper we prove that, locally, the annihilating ideal of 1/fk over DX is generated by linear differential operators of order 1 (for k big enough). For this purpose we prove a vanishing theorem for the extension groups of a certain logarithmic DX–module with OX. The logarithmic DX–module is naturally associated with D (see Notation 1.1). This result is related to the so called Logarithmic Comparison Theorem. |
Cita | Castro Jiménez, F.J., Gago Vargas, J., Hartillo Hermoso, I. y Ucha Enríquez, J.M. (2007). A vanishing theorem for a class of logarithmic D-modules. ArXiv.org, ArXiv:0707.1000 |
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