We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.
@article{bwmeta1.element.bwnjournal-article-apmv64z1p61bwm,
author = {Pawe\l\ Gniadek},
title = {On reconstruction of polynomial automorphisms},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {61-69},
zbl = {0860.14010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv64z1p61bwm}
}
Paweł Gniadek. On reconstruction of polynomial automorphisms. Annales Polonici Mathematici, Tome 63 (1996) pp. 61-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z1p61bwm/
[000] [A-E] K. Adjamagbo and A. van den Essen, A resultant criterion and formula for the inversion of a polynomial map in two variables, J. Pure Appl. Algebra 64 (1990), 1-6.
[001] [E] A. van den Essen, A criterion to decide if a polynomial map is invertible and to compute the inverse, Comm. Algebra 18 (1990), 3183-3186. | Zbl 0718.13008
[002] [E-K] A. van den Essen and M. Kwieciński, On the reconstruction of polynomial automorphisms from their face polynomials, J. Pure Appl. Algebra 80 (1992), 327-336. | Zbl 0763.14004
[003] [B] B. Buchberger, Gröbner bases: An algorithmic method in polynomial ideal theory, in: Multidimensional Systems Theory, N. Bose (ed.), Reidel, Dordrecht, 1985, 164-232. | Zbl 0587.13009
[004] [J1] Z. Jelonek, Identity sets for polynomial automorphisms, J. Pure Appl. Algebra 76 (1991), 333-337. | Zbl 0752.14010
[005] [J2] Z. Jelonek, Irreducible identity sets for polynomial automorphisms, Math. Z. 212 (1993), 601-617. | Zbl 0806.14011
[006] [K1] M. Kwieciński, A Gröbner basis criterion for isomorphisms of algebraic varieties, J. Pure Appl. Algebra 74 (1991), 275-279. | Zbl 0754.13021
[007] [K2] M. Kwieciński, Automorphisms from face polynomials via two Gröbner bases, J. Pure Appl. Algebra 82 (1992), 65-70. | Zbl 0805.13009
[008] [L-J] M. Lejeune-Jalabert, Effectivité de Calculs Polynomiaux, Cours de D.E.A., Univ. de Grenoble, 1986.
[009] J. McKay and S. Wang, An inversion formula for two polynomials in two variables, J. Pure Appl. Algebra 52 (1988), 103-119. | Zbl 0664.13001
[010] [P-P] F. Pauer and M. Pheifhofer, The theory of Gröbner bases, Enseign. Math. 34 (1988), 215-232.
[011] [W] T. Winiarski, Application of Gröbner bases in the theory of polynomial mappings, XIV Instructional Conf. in the Theory of Extremal Problems, Łódź Univ., 1993 (in Polish). | Zbl 0806.13009