Residue currents with prescribed annihilator ideals

Andersson, Mats; Wulcan, Elizabeth

Andersson, Mats ; Wulcan, Elizabeth

Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007), p. 985-1007 / Harvested from Numdam

Access to full text
Full (PDF)
Full (DJVU)

Publié le : 2007-01-01

MR 2419855 | Zbl 1143.32003 | 4 citations dans Numdam

DOI : https://doi.org/10.1016/j.ansens.2007.11.001

@article{ASENS_2007_4_40_6_985_0,
     author = {Andersson, Mats and Wulcan, Elizabeth},
     title = {Residue currents with prescribed annihilator ideals},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {40},
     year = {2007},
     pages = {985-1007},
     doi = {10.1016/j.ansens.2007.11.001},
     mrnumber = {2419855},
     zbl = {1143.32003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2007_4_40_6_985_0}
}

Andersson, Mats; Wulcan, Elizabeth. Residue currents with prescribed annihilator ideals. Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007) pp. 985-1007. doi : 10.1016/j.ansens.2007.11.001. http://gdmltest.u-ga.fr/item/ASENS_2007_4_40_6_985_0/

Bibliographie

[1] Andersson M., Residue currents and ideals of holomorphic functions, Bull. Sci. Math. 128 (2004) 481-512. | MR 2074610 | Zbl 1086.32005

[2] Andersson M., Ideals of smooth functions and residue currents, J. Funct. Anal. 212 (1) (2004) 76-88. | MR 2065238 | Zbl 1056.32006

[3] Andersson M., The membership problem for polynomial ideals in terms of residue currents, Ann. Inst. Fourier 56 (2006) 101-119. | Numdam | MR 2228682 | Zbl 1092.32002

[4] Andersson M., Residue currents of holomorphic morphisms, J. reine angew. Math. 596 (2006) 215-234. | MR 2254813 | Zbl 1106.32005

[5] Andersson M., Integral representation with weights II, division and interpolation formulas, Math. Z. 254 (2006) 315-332. | MR 2262705 | Zbl 1104.32002

[6] Bayer D., Mumford D., What can be computed in algebraic geometry?, in: Computational Algebraic Geometry and Commutative Algebra, Cortona, 1991, Sympos. Math., vol. XXXIV, Cambridge Univ. Press, Cambridge, 1993, pp. 1-48. | MR 1253986 | Zbl 0846.13017

[7] Bayer D., Peeva I., Sturmfels B., Monomial resolutions, Math. Res. Lett. 5 (1-2) (1998) 31-46. | Zbl 0909.13010

[8] Bayer D., Stillman M., A criterion for detecting m-regularity, Invent. Math. 87 (1987) 1-11. | MR 862710 | Zbl 0625.13003

[9] Bayer D., Sturmfels B., Cellular resolutions of monomial modules, J. reine angew. Math. 502 (1998) 123-140. | MR 1647559 | Zbl 0909.13011

[10] Berenstein C., Yger A., About L. Ehrenpreis fundamental principle, in: Geometrical and Algebraical Aspects in Several Complex Variables, Cetraro, 1989, Sem. Conf., vol. 8, EditEl, Rende, 1991, pp. 47-61. | MR 1222206 | Zbl 1112.32300

[11] Berenstein C., Yger A., Effective Bezout identities in $Q [z_{1}, \dots, z_{n}]$ , Acta Math. 166 (1991) 69-120. | MR 1088983 | Zbl 0724.32002

[12] Berenstein C., Gay R., Vidras A., Yger A., Residue Currents and Bézout Identities, Birkhäuser, 1993. | MR 1249478 | Zbl 0802.32001

[13] Berndtsson B., A formula for division and interpolation, Math. Ann. 263 (1983). | MR 707239 | Zbl 0499.32013

[14] Berndtsson B., Passare M., Integral formulas and an explicit version of the fundamental principle, J. Funct. Anal. 84 (1989). | MR 1001466 | Zbl 0686.46031

[15] Björk J.-E., Residues and $D$ -modules, in: The legacy of Niels Henrik Abel, Springer, Berlin, 2004, pp. 605-651. | MR 2077588 | Zbl 1069.32001

[16] Coleff N.R., Herrera M.E., Les courants résiduels associés à une forme méromorphe, Lect. Notes in Math., vol. 633, Springer-Verlag, Berlin-Heidelberg-New York, 1978. | Zbl 0371.32007

[17] Demailly J.P., Complex Analytic and Differential Geometry Monograph Grenoble, 1997.

[18] Dickenstein A., Sessa C., Canonical representatives in moderate cohomology, Invent. Math. 80 (1985) 417-434. | MR 791667 | Zbl 0556.32005

[19] Dickenstein A., Gay R., Sessa C., Yger A., Analytic functionals annihilated by ideals, Manuscripta Math. 90 (1996) 175-223. | MR 1391209 | Zbl 0871.32009

[20] Ehrenpreis L., Fourier Analysis in Several Complex Variables, Pure and Applied Mathematics, vol. XVII, Wiley-Interscience Publishers. A Division of John Wiley and Sons, New York-London-Sydney, 1970. | Zbl 0195.10401

[21] Eisenbud D., Commutative Algebra. With a View Toward Algebraic Geometry, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. | MR 1322960 | Zbl 0819.13001

[22] Eisenbud D., The Geometry of Syzygies. A Second Course in Commutative Algebra and Algebraic Geometry, Graduate Texts in Mathematics, vol. 229, Springer-Verlag, New York, 2005. | MR 2103875 | Zbl 1066.14001

[23] Griffiths Ph., Harris J., Principles of Algebraic Geometry, John Wiley and Sons, 1978. | MR 507725 | Zbl 0408.14001

[24] Gunning R., Rossi H., Analytic Functions of Several Complex Variables, Prentice-Hall Inc., Englewood Cliffs, NJ, 1965. | MR 180696 | Zbl 0141.08601

[25] Hörmander L., An Introduction to Complex Analysis in Several Variables, North-Holland Mathematical Library, vol. 7, Second revised edition, North-Holland Publishing Co., American Elsevier Publishing Co., Inc., Amsterdam-London/New York, 1973. | Zbl 0271.32001

[26] Hörmander L., The Analysis of Linear Partial Differential Operators I, second ed., Springer-Verlag, 1990. | Zbl 0712.35001

[27] Mayr E., Mayer A., The complexity of the word problem for commutative semigroups and polynomial ideals, Adv. Math. 46 (1982) 305-329. | MR 683204 | Zbl 0506.03007

[28] Miller E., Sturmfels B., Combinatorial Commutative Algebra, Graduate Texts in Mathematics, vol. 227, Springer-Verlag, New York, 2005. | MR 2110098 | Zbl 1090.13001 | Zbl 1066.13001

[29] Nöther M., Über einen Satz aus der Theorie der algebraischen Functionen, Math. Ann. (1873) 351-359. | JFM 05.0348.02 | MR 1509826

[30] Palamodov V.P., Linear Differential Operators with Constant Coefficients, Translated from the Russian by A.A. Brown, Die Grundlehren der mathematischen Wissenschaften, vol. 168, Springer-Verlag, New York-Berlin, 1970. | Zbl 0191.43401

[31] Passare M., Residues, currents, and their relation to ideals of holomorphic functions, Math. Scand. 62 (1988) 75-152. | MR 961584 | Zbl 0633.32005

[32] Yger A., Formules de division et prolongement méromorphe, in: Séminaire d'Analyse P. Lelong-P. Dolbeault-H. Skoda, Années 1985/1986, Lecture Notes in Math., vol. 1295, Springer, Berlin, 1987, pp. 226-283. | Zbl 0632.32010

[33] Passare M., Tsikh A., Yger A., Residue currents of the Bochner-Martinelli type, Publ. Mat. 44 (2000) 85-117. | Zbl 0964.32003

[34] Quillen D., Superconnections and the Chern character, Topology 24 (1985) 89-95. | MR 790678 | Zbl 0569.58030

[35] Shiffman B., Degree bounds for the division problem in polynomial ideals, Michigan Math. J. 36 (1989) 163-171. | MR 1000520 | Zbl 0691.12010

[36] Wulcan E., Residue currents of monomial ideals, Indiana Univ. J. 56 (2007) 36-388. | MR 2305939 | Zbl 1120.32004

[37] Wulcan E., Residue currents and their annihilator ideals, Thesis Gothenburg, 2007.