On some generalizations of Jacobi's residue formula
Annales scientifiques de l'École Normale Supérieure (2001)
- Volume: 34, Issue: 1, page 131-157
- ISSN: 0012-9593
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topVidras, Alekos, and Yger, Alain. "On some generalizations of Jacobi's residue formula." Annales scientifiques de l'École Normale Supérieure 34.1 (2001): 131-157. <http://eudml.org/doc/82537>.
@article{Vidras2001,
author = {Vidras, Alekos, Yger, Alain},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {compact complex variety; toric variety; Grothendieck residue; multidimensional residue; residual currents; Bochner-Martinelli formula; Nullstellensatz; Cayley-Bacharach theorems; Bézout identity; analytic continuation},
language = {eng},
number = {1},
pages = {131-157},
publisher = {Elsevier},
title = {On some generalizations of Jacobi's residue formula},
url = {http://eudml.org/doc/82537},
volume = {34},
year = {2001},
}
TY - JOUR
AU - Vidras, Alekos
AU - Yger, Alain
TI - On some generalizations of Jacobi's residue formula
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2001
PB - Elsevier
VL - 34
IS - 1
SP - 131
EP - 157
LA - eng
KW - compact complex variety; toric variety; Grothendieck residue; multidimensional residue; residual currents; Bochner-Martinelli formula; Nullstellensatz; Cayley-Bacharach theorems; Bézout identity; analytic continuation
UR - http://eudml.org/doc/82537
ER -
References
top- [1] Atiyah M.F., Resolution of singularities and division of distributions, Commun. Pure. Appl. Math.23 (1970) 145-150. Zbl0188.19405MR256156
- [2] Batyrev V., Cox D., On the Hodge structure of projective hypersurfaces in toric varieties, Duke J. Math.75 (1994) 293-338. Zbl0851.14021MR1290195
- [3] Bernstein D., The number of roots of a system of equations, Funct. Anal. Appl.9 (2) (1975) 183-185. Zbl0328.32001MR435072
- [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 I278 (1974) 949-951. Zbl0307.32007MR340642
- [5] Berenstein C.A., Yger A., A formula of Jacobi and its consequences, Ann. Scient. École Norm. Sup.24 (1991) 73-83. Zbl0742.32004
- [6] Berenstein C.A., Yger A., Residue calculus and effective Nullstellensatz, Amer. J. Math.121 (1999) 723-796. Zbl0944.14002MR1704477
- [7] Berenstein C.A., Yger A., Residues and effective Nullstellensatz, ERA Amer. Math. Soc.2 (2) (1996) 82-91. Zbl0872.14042MR1412946
- [8] Berenstein C.A., Yger A., Multidimensional residues and complexity problems, Mathematics and Computers in Simulation42 (1996) 449-457. Zbl1037.32502MR1430832
- [9] Cattani E., Cox D., Dickenstein A., Residues in toric varieties, Compositio Math.108 (1997) 35-76. Zbl0883.14029MR1458757
- [10] Cattani E., Dickenstein A., A global view of residues in the torus, J. Pure Appl. Algebra117 & 118 (1997) 119-144. Zbl0899.14024MR1457836
- [11] Cox D., The homogeneous coordinate ring of a toric variety, J. Algebraic Geom.4 (1995) 17-50. Zbl0846.14032MR1299003
- [12] Cox D., Recent developments in toric geometry, Proc. Symp. Pure Math., Vol. 62, Part 2, Amer. Math. Soc, Providence, RI, 1997. Zbl0899.14025MR1492541
- [13] Ein L., Lazarsfeld R., A geometric effective Nullstellensatz, Invent. Math.137 (1999) 427-448. Zbl0944.14003MR1705839
- [14] Eisenbud D., Green M., Harris J., Cayley–Bacharach theorems and conjectures, Bull. Amer. Math. Soc. (N.S.)33 (1996) 295-324. Zbl0871.14024
- [15] Ertl S., Hübl R., The Jacobian formula for Laurent polynomials, Universitatis Iagellonicae Acta MathematicaXXXVII (1999) 51-67. Zbl0989.14021MR1729520
- [16] Fabiano A., Pucci G., Yger A., Effective Nullstellensatz and geometric degree for zero-dimensional ideals, Acta Arithmetica78 (2) (1996) 165-187. Zbl0892.14002MR1424538
- [17] Fulton W., Introduction to Toric Varieties, Princeton Univ. Press, 1993. Zbl0813.14039MR1234037
- [18] Griffiths P., Harris J., Principles of Algebraic Geometry, Wiley Interscience, New York, 1978. Zbl0408.14001MR507725
- [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.
- [20] Kazarnovskii B.Ja., On the zeroes of exponential sums, Soviet. Math. Doklady23 (1981) 347-351. Zbl0491.32002MR612571
- [21] Kazarnovskii B.Ja., Newton polyhedra and zeros of systems of exponential sums, Funct. Anal. Appl.18 (4) (1984) 299-307. Zbl0593.32001MR775932
- [22] Khovanskii A., Newton polyhedra and the Euler–Jacobi formula, Russian Math. Surveys33 (1978) 237-238. Zbl0449.14010
- [23] Khovanskii A., Newton polyhedra and the toroidal varieties, Funct. Anal. Appl. (1978) 289-295. Zbl0445.14019
- [24] Kollár J., Sharp effective Nullstellensatz, J. Amer. Math. Soc.1 (1988) 963-975. Zbl0682.14001MR944576
- [25] Kollár J., Effective Nullstellensatz for arbitrary ideals, J. Eur. Math. Soc.1 (1999) 313-337. Zbl0986.14043MR1714736
- [26] Lipman J., Residues and traces of differential forms via Hochschild homology, Contemp. Math., 61, Amer. Math. Soc, Providence, 1987. Zbl0606.14015MR868864
- [27] Pellé T., Identités de Bézout pour certains systèmes de sommes d'exponentielles, Ark. Math.36 (1998) 131-162. Zbl0912.32003MR1611177
- [28] Passare M., Tsikh A., Yger A., Residue currents of the Bochner–Martinelli type, Publicaciones Math.44 (2000) 85-117. Zbl0964.32003
- [29] Tsikh A., Multidimensional residues and their applications, Transl. Amer. Math. Soc.103 (1992). Zbl0758.32001MR1181199
- [30] Varchenko A., Newton polyhedra and estimation of oscillating integrals, Funct. Anal. Appl.10 (1976) 175-196. Zbl0351.32011
- [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. Zbl0927.01018MR1487905
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