On Puiseux roots of Jacobians. (English) Zbl 1015.32025
Let \(f(x,y)\) and \(g(x,y)\) be holomorphic germs, \(f,g: (\mathbb{C}^2,0) \to(\mathbb{C},0)\).
The authors study properties of the zero arc \(x=\gamma(y)\) of the Jacobian determinant \(J(x,y)\) of \(f,g\) that it is not root of \(f\cdot g\).
The authors obtain the factorization of \(J(x,y)\) in \(\mathbb{C} \{x,y\}\).
The authors study properties of the zero arc \(x=\gamma(y)\) of the Jacobian determinant \(J(x,y)\) of \(f,g\) that it is not root of \(f\cdot g\).
The authors obtain the factorization of \(J(x,y)\) in \(\mathbb{C} \{x,y\}\).
Reviewer: P.Z.Agranovich (Khar’kov)
References:
| [1] | Garcia-Barroso, E.: Sur les courbes polaires d’une courbe plane réduite. Proc. London Math. Soc. (3), 81 , 1-28 (2000). · Zbl 1041.14008 · doi:10.1112/S0024611500012430 |
| [2] | Izumi, S., Koike, S., and Kuo, T.-C.: Computations and stability of the Fukui invariants. Compositio Math., 130 , 49-73 (2002). · Zbl 1007.58023 · doi:10.1023/A:1013784111756 |
| [3] | Kuo, T.-C., and Lu, Y.C.: On analytic function germs of two complex variables. Topology, 16 , 299-310 (1977). · Zbl 0378.32001 · doi:10.1016/0040-9383(77)90037-4 |
| [4] | Kuo, T.-C., and Parusiński, A.: Newton polygon relative to an arc. Real and Complex Sin- gularities (São Carlos, 1998) (eds. Bruce, J.W., and Tari, F.). Chapman and Hall Res. Notes Math. no. 412, Chapman and Hall, Boca Raton-London-New York-Washington D.C., pp. 76-93 (2000). |
| [5] | Merle, M.: Invariants polaires des courbes planes. Invent. Math., 41 , 299-310 (1977). · Zbl 0371.14003 · doi:10.1007/BF01418370 |
| [6] | Pham, F.: Deformations equisingularitiés des ideaux jacobiens de courbes planes. Proc. Liverpool Singularities Symposium, II (ed. Wall C.T.C.). Lecture Notes in Math. vol. 209, Springer-Verlag, Berlin-Heidelberg-New York, pp. 218-233 (1971). · doi:10.1007/BFb0068907 |
| [7] | Walker, R. J.: Algebraic Curves. Springer-Verlag, Berlin-Heidelberg-New York (1972). |
| [8] | Zariski, O.: Studies in equisingularity I. Amer J. Math. 2, 87 , 507-536 (1965). · Zbl 0132.41601 · doi:10.2307/2373019 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
