A criterion for the logarithmic differential operators to be generated by vector fields
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Abstract:
We study divisors in a complex manifold in view of the property that the algebra of logarithmic differential operators along the divisor is generated by logarithmic vector fields. We give
a sufficient criterion for the property,
a simple proof of F.J. Calderón-Moreno’s theorem that free divisors have the property,
a proof that divisors in dimension $3$ with only isolated quasi-homogeneous singularities have the property,
an example of a nonfree divisor with nonisolated singularity having the property,
an example of a divisor not having the property, and
an algorithm to compute the V-filtration along a divisor up to a given order.
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Additional Information
- Mathias Schulze
- Affiliation: Department of Mathematics, Oklahoma State University, 401 MSCS, Stillwater, Oklahoma 74078
- Email: mschulze@math.okstate.edu
- Received by editor(s): September 16, 2005
- Received by editor(s) in revised form: September 2, 2006
- Published electronically: August 7, 2007
- Additional Notes: The author is grateful to M. Granger for many valuable discussions and comments and to F.J. Castro-Jiménez, L. Narváez-Macarro, and J.M. Ucha-Enríquez for explaining their results and ideas.
- Communicated by: Michael Stillman
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3631-3640
- MSC (2000): Primary 32C38, 13A30
- DOI: https://doi.org/10.1090/S0002-9939-07-08969-1
- MathSciNet review: 2336579