Open Access
April, 2016 On the blow-analytic equivalence of tribranched plane curves
Cristina VALLE
J. Math. Soc. Japan 68(2): 823-838 (April, 2016). DOI: 10.2969/jmsj/06820823


We prove the finiteness of the number of blow-analytic equivalence classes of embedded plane curve germs for any fixed number of branches and for any fixed value of $\mu'$ —a combinatorial invariant coming from the dual graphs of good resolutions of embedded plane curve singularities. In order to do so, we develop the concept of standard form of a dual graph. We show that, fixed $\mu'$ in $\mathbb{N}$, there are only a finite number of standard forms, and to each one of them correspond a finite number of blow-analytic equivalence classes. In the tribranched case, we are able to give an explicit upper bound to the number of graph standard forms. For $\mu'\leq 2$, we also provide a complete list of standard forms.


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Cristina VALLE. "On the blow-analytic equivalence of tribranched plane curves." J. Math. Soc. Japan 68 (2) 823 - 838, April, 2016.


Published: April, 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1343.32005
MathSciNet: MR3488148
Digital Object Identifier: 10.2969/jmsj/06820823

Primary: 32S15
Secondary: 14B05 , 14P15

Keywords: blow-analytic equivalence , dual graph to a resolution , local singularities , real plane curves

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 2 • April, 2016
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