Residue currents and complexity problems

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1. [Ai] L. A. Aizenberg and A. P. Yuzhakov, Integral Representation and Residues in Multidimensional Complex Analysis, Amer. Math. Soc., Providence, 1983. 
2. [Am] F. Amoroso, Bounds for the degrees in the membership test for a polynomial ideal, Acta Arith. 56 (1990), 19-24. 
3. [Am1] F. Amoroso, Tests d'appartenance d'après un théorème de J. Kollar, C. R. Acad. Sci. Paris Sér. I 309 (1989), 691-694. Zbl0703.13003
4. [Am2] F. Amoroso, Membership problem, in: Diophantine Approximations and Transcendental Numbers, Luminy 1990, P. Philippon (ed.), Walter de Gruyter, Berlin, 1992, 15-37. 
5. [Am3] F. Amoroso, On a conjecture of C. Berenstein and A. Yger, in: Proc. MEGA 94, Progr. Math., Birkhäuser, to appear. 
6. [Am4] F. Amoroso, The membership problem for smooth ideals, Publ. Math. Univ. P. et M. Curie, to appear. 
7. [Am5] F. Amoroso, The membership problem for 'almost' complete intersection ideals, preprint. 
8. [At] M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math. 23 (1970), 145-150. Zbl0188.19405
9. [BaS] D. Bayer and M. Stillman, On the complexity of computing syzygies, J. Symbolic Comp. 6 (1988), 135-147. Zbl0667.68053
10. [BGVY] C. A. Berenstein, R. Gay, A. Vidras and A. Yger, Residue Currents and Bézout Identities, Progr. Math. 114, Birkhäuser, 1993. 
11. [BT] C. A. Berenstein and B. A. Taylor, Interpolation problems in ${ℂ}^n$ with applications to harmonic analysis, J. Analyse Math. 38 (1980), 188-254. Zbl0464.42003
12. [BY1] C. A. Berenstein and A. Yger, Bounds for the degrees in the division problem, Michigan Math. J. 37 (1990), 26-44. 
13. [BY2] C. A. Berenstein and A. Yger, Effective Bézout identities in $\mathbb{Q}[z_1,...,z_n]$, Acta Math. 166 (1991), 69-120. Zbl0724.32002
14. [BY3] C. A. Berenstein and A. Yger, Une formule de Jacobi et ses conséquences, Ann. Sci. Ecole. Norm. Sup. 24 (1991), 363-377. Zbl0742.32004
15. [BY4] C. A. Berenstein and A. Yger, Formules de représentation intégrale et problèmes de division, in: Diophantine Approximations and Transcendental Numbers, P. Philippon (ed.), Walter de Gruyter, Berlin, 1992, 15-37. Zbl0765.32002
16. [BY5] C. A. Berenstein and A. Yger, Bounds for the division problem, in: Proc. Sympos. Pure Math. 52, part 1, Amer. Math. Soc., 1991, 22-28. 
17. [BGS1] J. B. Bost, H. Gillet et C. Soulé, Un analogue arithmétique du théorème de Bézout, C. R. Acad. Sci. Paris Sér. I 312 (1991), 845-848. 
18. [BGS2] J. B. Bost, H. Gillet et C. Soulé, Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (1994), 903-1027. Zbl0973.14013
19. [Br1] W. D. Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of Math. 126 (1987), 577-591. Zbl0641.14001
20. [Br2] W. D. Brownawell, Local diophantine Nullstellen inequalities, J. Amer. Math. Soc. 1 (1988), 311-322. Zbl0651.10022
21. [Br3] W. D. Brownawell, Distance to common zeros and lower bounds for polynomials, in: Diophantine Approximations and Transcendental Numbers, Luminy 1990, P. Philippon (ed.), Walter de Gruyter, Berlin, 1992, 51-64. 
22. [Br4] W. D. Brownawell, A prime power version of the Nullstellensatz, Michigan Math. J., to appear. 
23. [Elk1] M. Elkadi, Une version effective du théorème de Briançon-Skoda dans le cas algébrique discret, Acta Arith. 66 (1994), 201-220. 
24. [Elk2] M. Elkadi, Bornes pour les degrés et les hauteurs dans le problème de division, Michigan Math. J., to appear. 
25. [Fa] G. Faltings, Diophantine approximation on Abelian varieties, Ann. of Math. 133 (1991), 549-576. Zbl0734.14007
26. [GH] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. Zbl0408.14001
27. [GS] H. Gillet and C. Soulé, Arithmetic intersection theory, Publ. Math. I.H.E.S. 72 (1990), 93-174. Zbl0741.14012
28. [HP] W. V. D. Hodge and D. Pedoe, An Introduction to Algebraic Geometry, 3 Volumes, Cambridge University Press, Cambridge, 1952. 
29. [Jac] C. G. J. Jacobi, Theoremata nova algebraica circa systema duarum aequationum inter duas variabiles propositarum, in: Gesammelte Werke, Band III, 285-294. 
30. [Ko] J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988), 963-975. 
31. [Ky] A. M. Kytmanov, A transformation formula for Grothendieck residues and some of its applications, Siberian Math. J. 1989, 495-499. 
32. [LT] J. Lipman and B. Teissier, Pseudorational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981), 97-115. Zbl0464.13005
33. [Mac] F. S. Macaulay, The Algebraic Theory of Modular Systems, Cambridge University Press, Cambridge, 1916. 
34. [MaM] E. Mayr and A. Meyer, The complexity of the word problem for commutative semigroups and polynomial ideals, Adv. in Math. 127 (1988), 305-329. 
35. [Ph1] P. Philippon, Critères pour l'indépendance algébrique, Publ. Math. I.H.E.S. 64 (1986), 5-52. 
36. [Ph2] P. Philippon, A propos du texte de W.D. Brownawell: 'Bounds for the degrees in the Nullstellensatz', Ann. of Math. 127 (1988), 367-371. 
37. [Ph3] P. Philippon, Dénominateurs dans le théorème des zéros de Hilbert, Acta Arith. 58 (1991), 1-25. Zbl0679.13010
38. [Ph4] P. Philippon, Sur des hauteurs alternatives I, Math. Ann. 289 (1991), 255-283. Zbl0726.14017
39. [Sk] H. Skoda, Application des techniques L${}^2$ à la théorie des idéaux d’une algèbre de fonctions holomorphes avec poids, Ann. Sci. Ecole. Norm. Sup. 5 (1972), 545-579. Zbl0254.32017
40. [St] W. Stoll, About the value distribution of holomorphic maps into projective space, Acta Math. 123 (1969), 83-114. Zbl0177.11302
41. [Ts] A. Tsikh, Multidimensional Residues and Their Applications, Transl. Math. Monographs, Amer. Math. Soc., 1992. 
42. [Weil] A. Weil, L'intégrale de Cauchy et les fonctions de plusieurs variables, Math. Ann. 111 (1935), 178-182. Zbl0011.12301
43. [Y] A. Yger, Résidus, courants résiduels et courants de Green, in: Actes du Colloque de Géométrie Analytique, Paris VII, 1992, Travaux en Cours, Hermann, Paris, to appear. 

1. A. Fabianom, G. Pucci, A. Yger, Effective Nullstellensatz and geometric degree for zero-dimensional ideals