Some Reductions on Jacobian Problem in Two Variables
| dc.creator | Zhao, Wenhua | |
| dc.date | 2002-09-19 | |
| dc.date.accessioned | 2026-07-07T12:38:21Z | |
| dc.date.available | 2026-07-07T12:38:21Z | |
| dc.description | Let $f=(f_1, f_2)$ be a regular sequence of affine curves in $\bC^2$. Under some reduction conditions achieved by composing with some polynomial automorphisms of $\bC^2$, we show that the intersection number of curves $(f_i)$ in $\bC^2$ equals to the coefficient of the leading term $x^{n-1}$ in $g_2$, where $n=°f_i$ $(i=1, 2)$ and $(g_1, g_2)$ is the unique solution of the equation $y{\mathcal J}(f)=g_1f_1+g_2f_2$ with $°g_i\leq n-1$. So the well-known Jacobian problem is reduced to solving the equation above. Furthermore, by using the result above, we show that the Jacobian problem can also be reduced to a special family of polynomial maps. | |
| dc.identifier | https://arxiv.org/abs/math/0209254 | |
| dc.identifier | http://arxiv.org/abs/math/0209254 | |
| dc.identifier | J. Pure Appl. Algebra, 188 (2004), no. 1-3, 305--319. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218731 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Complex Variables | |
| dc.subject | 14R15, 14C17 | |
| dc.title | Some Reductions on Jacobian Problem in Two Variables | |
| dc.type | text |