Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal forms of foliations and curves defined by a function with a
  generic tangent cone   We first describe the local and global moduli spaces of germs of foliations
defined by analytic functions in two variables with p transverse smooth
branches, and with integral multiplicities (in the univalued holomorphic case)
or complex multiplicities (in the multivalued ''Darboux'' case). We specify
normal forms in each class. Then we study on these moduli space the
distribution C induced by the following equivalence relation: two points are
equivalent if and only if the corresponding foliations have the same analytic
invariant curves up to analytical conjugacy. Therefore, the space of leaves of
C is the moduli space of curves. We prove that C is rationally integrable.
These rational integrals give a complete system of invariants for these generic
plane curves, which extend the well-known cross-ratios between branches.

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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: eess