Newton-Puiseux Roots of Jacobian Determinants
| dc.creator | Kuo, Tzee-Char | |
| dc.creator | Parusinski, Adam | |
| dc.date | 2002-11-26 | |
| dc.date.accessioned | 2026-07-07T04:53:18Z | |
| dc.date.available | 2026-07-07T04:53:18Z | |
| dc.description | Let $f(x,y), g(x,y)$ denote either a pair of holomorphic function germs, or a pair of monic polynomials in $x$ whose coefficients are Laurent series in $y$. A relative polar arc is a Newton-Puiseux root, $x=γ(y)$, of the Jacobian $J=f_yg_x-f_xg_y$. We define the tree-model, $T(f,g)$, for the pair, using the contact orders of the Newton-Puiseux roots of $f$ and $g$. We then describe how the $γ$'s climb, and where they leave, the tree. We shall also show by two examples that the way the $γ$'s leave the tree is not an invariant of the tree; this phenomenon is in sharp contrast to that in the one function case where the tree completely determines how the polar roots split away. Our result yield a factorisation of the Jacobian determinant. | |
| dc.description | 19 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0211408 | |
| dc.identifier | http://arxiv.org/abs/math/0211408 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65795 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32S05, 14H20 | |
| dc.title | Newton-Puiseux Roots of Jacobian Determinants | |
| dc.type | text |