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INDECOMPOSABLE NON-HOLONOMIC $\mathcal{D}$-MODULES IN DIMENSION $2$

Published online by Cambridge University Press:  04 July 2003

S. C. Coutinho
S. C. Coutinho
Affiliation:
Departamento de Ciência da Computação, Instituto de Matemática, Universidade Federal do Rio de Janeiro, PO Box 68530, 21945-970 Rio de Janeiro, Brazil ([email protected])
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Abstract

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A module of a ring of differential operators $\mathcal{D}$ over a smooth surface has order $1$ if it is isomorphic to a factor module of $\mathcal{D}$ by a cyclic ideal generated by an operator of order $1$. Let $k$ be a positive integer. We give conditions under which an indecomposable $\mathcal{D}$-module of order $1$ is GK-critical of length $k$. We also give examples of indecomposable, non-critical, $\mathcal{D}$-modules whose subfactors have order $1$.

AMS 2000 Mathematics subject classification: Primary 16S32. Secondary 37F75

Keywords

modulering of differential operatorscritical module
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 341 - 355
Copyright
Copyright © Edinburgh Mathematical Society 2003