2026-06-07T15:51:28Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/422472023-08-25T11:31:27Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
González Pérez, Pedro Daniel
2023-06-20T00:14:13Z
2023-06-20T00:14:13Z
2010-07
0025-5645
10.2969/jmsj/06230975
https://hdl.handle.net/20.500.14352/42247
http://projecteuclid.org/euclid.jmsj/1280496827
http://projecteuclid.org
We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of C{x}[y], defining a plane branch (C, 0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branch (C, 0) supported on certain monomials in the approximate roots of f, which are essential in the study of Harnack smoothings of real plane branches by Risler and the author. Our results provide also a geometrical approach to Abhyankar's irreducibility criterion for power series in two variables and also a criterion to determine if a family of plane curves is equisingular to a plane branch.
eng
Approximate roots, toric resolutions and deformations of a plane branch
journal article
URL
https://docta.ucm.es/bitstreams/74073ae7-4555-4886-92e2-94ab6a2a51d5/download
File
MD5
ca4a36f9fca59bd3c47c53bc67f67143
318793
application/pdf
GPerez_Pedro01.pdf
URL
https://docta.ucm.es/bitstreams/771359d6-047b-4f61-9eee-330950abb27f/download
File
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15d27a0c0bd1adc8fc4ae3a470e02235
69242
text/plain
GPerez_Pedro01.pdf.txt