Effective Nullstellensatz and geometric degree for zero-dimensional ideals

A. Fabianom; G. Pucci; A. Yger

ArticleOriginal scientific text

Title

Effective Nullstellensatz and geometric degree for zero-dimensional ideals

Authors ¹, ¹, ²

Affiliations

Dipartimento di Matematica, Università della Calabria, Arcavacata di Rende (Cs), Italy
Département de Mathématiques, Université Bordeaux I, 33405, Talence, France

[Aiz] L. A. Aizenberg, Multidimensional logarithmic residues and their applications, in: Several Complex Variables II, Encyclopaedia Math. Sci. 8, Springer, 1994, 24-39.
[Ban] C. Banica and O. Stănăşila, Algebraic Methods in the Global Theory of Complex Spaces, Wiley, New York, 1976.
[BGVY] C. A. Berenstein, R. Gay, A. Vidras and A. Yger, Residue Currents and Bézout Identities, Progr. Math. 114, Birkhäuser, Basel, 1993.
[BY1] C. A. Berenstein and A. Yger, Effective Bézout identities in $ℚ [z ₁, ..., z_{n}]$ , Acta Math. 166 (1991), 69-120.
[BY2] C. A. Berenstein and A. Yger, Une formule de Jacobi et ses conséquences, Ann. Sci. École Norm. Sup. Paris 24 (1991), 363-377.
[Bie1] G. Biernat, On the sum of residues for a polynomial mapping, Bull. Soc. Sci. Lett. Łódź 40, Sér. Rech. Déform. 9 (1990), 73-83.
[Bie2] G. Biernat, On the Jacobi-Kronecker formula for a polynomial mapping having zeroes at infinity, Bull. Soc. Sci. Lett. Łódź 42, Sér. Rech. Déform. 14 (1992/93), 103-111.
[BS] J. Briançon et H. Skoda, Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de $ℂ^{n}$ , C. R. Acad. Sci. Paris Sér. A Math. 278 (1974), 949-951.
[Br1] D. W. Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of Math. 126 (1987), 577-591.
[Br2] D. W. Brownawell, A prime power version of the Nullstellensatz, preprint, 1989.
[CN] P. Cassou-Noguès, Quelques remarques sur les applications polynomiales propres, manuscript, 1994.
[CNPł] P. Cassou-Noguès et A. Płoski, Un théorème des zéros effectif, Bull. Polish Acad. Sci. 44 (1996), 61-70.
[CoS] D. Cox, J. Little and D. O'Shea, Ideals, Varieties and Algorithms, Undergrad. Texts Math., Springer, 1991.
[ElY] M. Elkadi and A. Yger, Residue currents and complexity problems, in: Topics in Complex Analysis, Banach Center Publ. 31, Inst. Math., Polish Acad. Sci., Warszawa, 1995, 173-186.
[Fi] N. Fitchas et A. Galligo, Nullstellensatz effectif et conjecture de Serre (théorème de Quillen-Suslin) pour le Calcul Formel, Math. Nachr. 149 (1990), 231-253.
[HGi] M. Giusti, J. Heintz, J. E. Morais and L. M. Pardo, When polynomial equation systems can be 'solved' fast, preprint, Laboratoire GAGE, École Polytechnique, 1995.
[GH] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, New York, 1978.
[Je] Z. Jelonek, The set of points at which a polynomial map is not proper, Ann. Polon. Math. 48 (1993), 259-266.
[K] J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988), 963-975.
[LT] J. Lipman and B. Teissier, Pseudo-rational local rings and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1991), 97-116.
[Pe] O. Perron, Algebra I (Die Grundlagen), Göschens Lehrbücherei, Berlin und Leipzig, 1932.
[Pł1] A. Płoski, On the growth of proper polynomial mappings, Ann. Polon. Math. 45 (1985), 287-309.
[Pł2] A. Płoski, Sur l'exposant d'une application analytique I, Bull. Polish Acad. Sci. Math. 32 (1984), 669-673.
[PłT] A. Płoski and P. Tworzewski, A separation condition for polynomial mappings, Bull. Polish Acad. Sci. Math. 44 (1996), to appear.
[T] B. Teissier, Résultats récents d'algèbre commutative effective, Séminaire Bourbaki, 1989/1990, exposé 718, Astérisque 189-190 (1990), 107-131.
[Y] A. Yger, Courants résidus et applications, Publications de l'Ecole Doctorale, Bordeaux, 1994.

Title

Effective Nullstellensatz and geometric degree for zero-dimensional ideals

Affiliations

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