Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincar\'e series for filtrations defined by discrete valuations with
  arbitrary center   To study singularities on complex varieties we study Poincar\'e series of
filtrations that are defined by discrete valuations on the local ring at the
singularity. In all previous papers on this topic one poses restrictions on the
centers of these valuations and often one uses several definitions for
Poincar\'e series. In this article we show that these definitions can differ
when the centers of the valuations are not zero-dimensional, i.e. do not have
the maximal ideal as center. We give a unifying definition for Poincar\'e
series which also allows filtrations defined by valuations that are all
nonzero-dimensional. We then show that this definition satisfies a nice
relation between Poincar\'e series for embedded filtrations and Poincar\'e
series for the ambient space and we give some application for singularities
which are nondegenerate with respect to their Newton polyhedron.

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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg