Decompositions of the higher order polars of plane branches
-
Evelia R. García Barroso
and
Janusz Gwoździewicz
Abstract
In [1] Casas-Alvero found decompositions of higher order polars of an irreducible plane complex analytic curve generalizing the results of Merle. We improve his result obtaining a finer decomposition where we find out a kind of branches that we call threshold semi-roots. The existence of threshold semi-roots is a new phenomenon observed for the higher order polars. The topological type and the number of these branches is determined by the topological type of the original curve.
Funding source: Ministerio de Economía y Competitividad
Award Identifier / Grant number: MTM2012-36917-C03-01
Funding statement: The first-named author was partially supported by the Spanish Project MTM2012-36917-C03-01 and the second author was partially supported by the Plan Propio de Investigación de la Universidad de La Laguna-2014.
Acknowledgements
The authors thank Bernard Teissier for suggesting the name threshold semi-root.
References
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Articles in the same Issue
- Frontmatter
- A note on the Hilali conjecture
- Finite groups have more conjugacy classes
- The gauge action, DG Lie algebras and identities for Bernoulli numbers
- Unitary embeddings of finite loop spaces
- Topological complexity of planar polygon spaces with small genetic code
- Numerical semigroups in a problem about cost-effective transport
- On the smallest simultaneous power nonresidue modulo a prime
- Decompositions of the higher order polars of plane branches
- A formula for the expected volume of the Wiener sausage with constant drift
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The slice spectral sequence for the
- Incidences between points and generalized spheres over finite fields and related problems
- Mean values of the Witten L-function for SU(2)
- A direct computation of the cohomology of the braces operad
- Abelian varieties over finite fields as basic abelian varieties
