On Puiseux roots of Jacobians
Kuo, Tzee-Char ; Parusi\'{n}ski, Adam
Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, p. 55-59 / Harvested from Project Euclid
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Take holomorphic $f(x,y)$, $g(x,y)$. A polar arc is a Puiseux root, $x = \gamma(y)$, of the Jacobian $J = f_y g_x - f_x g_y$, but not one of $f \cdot g$. We define the tree, $T(f,g)$, using the contact orders of the roots of $f \cdot g$, describe how polar arcs climb, and leave, the tree, and how to factor $J$ in $\mathbf{C}\{x,y\}$. When collinear points/bars exist, the way the $\gamma$'s leave the tree is not an invariant.
Publié le : 2002-05-14
Classification:  Puiseux roots,  polar arcs,  Jacobian,  32S05,  14H20 
@article{1148392712,
     author = {Kuo, Tzee-Char and Parusi\'{n}ski, Adam},
     title = {On Puiseux roots of Jacobians},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {78},
     number = {10},
     year = {2002},
     pages = { 55-59},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148392712}
}

Kuo, Tzee-Char; Parusi\'{n}ski, Adam. On Puiseux roots of Jacobians. Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, pp.  55-59. http://gdmltest.u-ga.fr/item/1148392712/