Let $p$ and $q$ be integers such that $p > q \geq 2$ and $q$ divides $p$ . Let $\varphi (q)$ be the Euler number of $q$ . We exhibit a Zariski $\varphi(q)$ -ple, distinguished by the Alexander polynomial, whose curves are tame torus curves of type $(p,q)$ , with $q$ smooth irreducible components of degree $p$ ,and one single singular point topologically equivalent to the Brieskorn-Pham singularity $v^q+u^{qp^2}=0$ .
Publié le : 2005-10-14
Classification:
Torus curves,
maximal contact,
Alexander polynomial,
Zariski multiple,
14H20,
14H30,
32S05,
32S55
@article{1150287300,
author = {AUDOUBERT, Beno\^\i t and NGUYEN, Tu Chanh and OKA, Mutsuo},
title = {On Alexander polynomials of torus curves},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 935-957},
language = {en},
url = {http://dml.mathdoc.fr/item/1150287300}
}
AUDOUBERT, Benoît; NGUYEN, Tu Chanh; OKA, Mutsuo. On Alexander polynomials of torus curves. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 935-957. http://gdmltest.u-ga.fr/item/1150287300/