Abstract
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.
Citation
Cristina VALLE. "On the blow-analytic equivalence of tribranched plane curves." J. Math. Soc. Japan 68 (2) 823 - 838, April, 2016. https://doi.org/10.2969/jmsj/06820823
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