On some generalizations of Jacobi's residue formula
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 1, pp. 131-157.
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     author = {Vidras, Alekos and Yger, Alain},
     title = {On some generalizations of {Jacobi's} residue formula},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {131--157},
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     volume = {Ser. 4, 34},
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     year = {2001},
     doi = {10.1016/s0012-9593(00)01056-9},
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     zbl = {0991.32003},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(00)01056-9/}
}
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Vidras, Alekos; Yger, Alain. On some generalizations of Jacobi's residue formula. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 1, pp. 131-157. doi : 10.1016/s0012-9593(00)01056-9. http://archive.numdam.org/articles/10.1016/s0012-9593(00)01056-9/

[1] Atiyah M.F., Resolution of singularities and division of distributions, Commun. Pure. Appl. Math. 23 (1970) 145-150. | MR | Zbl

[2] Batyrev V., Cox D., On the Hodge structure of projective hypersurfaces in toric varieties, Duke J. Math. 75 (1994) 293-338. | MR | Zbl

[3] Bernstein D., The number of roots of a system of equations, Funct. Anal. Appl. 9 (2) (1975) 183-185. | MR | Zbl

[4] Briançon J., Skoda H., Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de Cn, C. R. Acad. Sci. Paris, Série I 278 (1974) 949-951. | MR | Zbl

[5] Berenstein C.A., Yger A., A formula of Jacobi and its consequences, Ann. Scient. École Norm. Sup. 24 (1991) 73-83. | Numdam | MR | Zbl

[6] Berenstein C.A., Yger A., Residue calculus and effective Nullstellensatz, Amer. J. Math. 121 (1999) 723-796. | MR | Zbl

[7] Berenstein C.A., Yger A., Residues and effective Nullstellensatz, ERA Amer. Math. Soc. 2 (2) (1996) 82-91. | EuDML | MR | Zbl

[8] Berenstein C.A., Yger A., Multidimensional residues and complexity problems, Mathematics and Computers in Simulation 42 (1996) 449-457. | MR | Zbl

[9] Cattani E., Cox D., Dickenstein A., Residues in toric varieties, Compositio Math. 108 (1997) 35-76. | MR | Zbl

[10] Cattani E., Dickenstein A., A global view of residues in the torus, J. Pure Appl. Algebra 117 & 118 (1997) 119-144. | MR | Zbl

[11] Cox D., The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995) 17-50. | MR | Zbl

[12] Cox D., Recent developments in toric geometry, Proc. Symp. Pure Math., Vol. 62, Part 2, Amer. Math. Soc, Providence, RI, 1997. | MR | Zbl

[13] Ein L., Lazarsfeld R., A geometric effective Nullstellensatz, Invent. Math. 137 (1999) 427-448. | MR | Zbl

[14] Eisenbud D., Green M., Harris J., Cayley-Bacharach theorems and conjectures, Bull. Amer. Math. Soc. (N.S.) 33 (1996) 295-324. | Zbl

[15] Ertl S., Hübl R., The Jacobian formula for Laurent polynomials, Universitatis Iagellonicae Acta Mathematica XXXVII (1999) 51-67. | MR | Zbl

[16] Fabiano A., Pucci G., Yger A., Effective Nullstellensatz and geometric degree for zero-dimensional ideals, Acta Arithmetica 78 (2) (1996) 165-187. | MR | Zbl

[17] Fulton W., Introduction to Toric Varieties, Princeton Univ. Press, 1993. | MR | Zbl

[18] Griffiths P., Harris J., Principles of Algebraic Geometry, Wiley Interscience, New York, 1978. | MR | Zbl

[19] Jacobi C.G.J., De relationibus, quae locum habere denent inter puncta intersectionis duarum curvarum vel trium superficierum algebraicarum dati ordinis, simul cum enodatione paradoxi algebraici, Gesammelte Werke, Band III, pp. 329-354. | Zbl

[20] Kazarnovskii B.Ja., On the zeroes of exponential sums, Soviet. Math. Doklady 23 (1981) 347-351. | MR | Zbl

[21] Kazarnovskii B.Ja., Newton polyhedra and zeros of systems of exponential sums, Funct. Anal. Appl. 18 (4) (1984) 299-307. | MR | Zbl

[22] Khovanskii A., Newton polyhedra and the Euler-Jacobi formula, Russian Math. Surveys 33 (1978) 237-238. | Zbl

[23] Khovanskii A., Newton polyhedra and the toroidal varieties, Funct. Anal. Appl. (1978) 289-295. | Zbl

[24] Kollár J., Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988) 963-975. | MR | Zbl

[25] Kollár J., Effective Nullstellensatz for arbitrary ideals, J. Eur. Math. Soc. 1 (1999) 313-337. | MR | Zbl

[26] Lipman J., Residues and traces of differential forms via Hochschild homology, Contemp. Math., 61, Amer. Math. Soc, Providence, 1987. | MR | Zbl

[27] Pellé T., Identités de Bézout pour certains systèmes de sommes d'exponentielles, Ark. Math. 36 (1998) 131-162. | MR | Zbl

[28] Passare M., Tsikh A., Yger A., Residue currents of the Bochner-Martinelli type, Publicaciones Math. 44 (2000) 85-117. | Zbl

[29] Tsikh A., Multidimensional residues and their applications, Transl. Amer. Math. Soc. 103 (1992). | MR | Zbl

[30] Varchenko A., Newton polyhedra and estimation of oscillating integrals, Funct. Anal. Appl. 10 (1976) 175-196. | Zbl

[31] Yger A., Lectures at Croce di Magara, June 1998, notes, available on the site www.math.u-bordeaux.fr/~yger.

[32] Yger A., Résidus, courants résiduels et courants de Green, in: Norguet F., Ofman S., Szczeciniarz J.J. (Eds.), Géométrie Complexe, Actualités Scientifiques et Industrielles, 1438, Hermann, Paris, 1996. | MR | Zbl

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