Open Access
May 2002 On Puiseux roots of Jacobians
Tzee-Char Kuo, Adam Parusi\'{n}ski
Proc. Japan Acad. Ser. A Math. Sci. 78(5): 55-59 (May 2002). DOI: 10.3792/pjaa.78.55


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.


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Tzee-Char Kuo. Adam Parusi\'{n}ski. "On Puiseux roots of Jacobians." Proc. Japan Acad. Ser. A Math. Sci. 78 (5) 55 - 59, May 2002.


Published: May 2002
First available in Project Euclid: 23 May 2006

zbMATH: 1015.32025
MathSciNet: MR1905388
Digital Object Identifier: 10.3792/pjaa.78.55

Primary: 14H20 , 32S05

Keywords: Jacobian , polar arcs , Puiseux roots

Rights: Copyright © 2002 The Japan Academy

Vol.78 • No. 5 • May 2002
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