Abstract
In this article we define a Poincare series on a subspace of a complex analytic germ, induced by a multi-index filtration on the ambient space. This Poincare series differs from Poincare series studied before in the sense that there is no notion of fibre that corresponds to our Poincare series. We compute this Poincare series for subspaces defined by principal ideals. For plane curve singularities and nondegenerate singularities this Poincare series yields topological and geometric information. We compare this Poincare series with the one introduced in [E,G-Z2]. In few cases they are equal and we show that the Poincare series we consider in this paper in general yields more information.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
