Algebraization of codimension one webs [after Trépreau, Hénaut, Pirio, Robert, ...]

Pereira, Jorge Vitório

Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 974, 26 p.

Zbl | 1 citation dans Numdam

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     author = {Pereira, Jorge Vit\'orio},
     title = {Algebraization of codimension one webs [after {Tr\'epreau,} {H\'enaut,} {Pirio,} {Robert,} ...]},
     booktitle = {S\'eminaire Bourbaki - Volume 2006/2007  - Expos\'es 967-981},
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     pages = {243--268},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {317},
     year = {2008},
     zbl = {1184.14014},
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     url = {http://www.numdam.org/item/AST_2008__317__243_0/}
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Pereira, Jorge Vitório. Algebraization of codimension one webs [after Trépreau, Hénaut, Pirio, Robert, ...], dans Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 974, 26 p. http://www.numdam.org/item/AST_2008__317__243_0/

Bibliographie
Cité par

[1] N. Abel - "Méthode générale pour trouver des fonctions d'une seule quantité variable lorsqu'une propriété de ces fonctions est exprimée par une équation entre deux variables", in Œuvres complètes de N. H. Abel, tome 1, Grøndhal & Son, 1981, p. 1-10.

[2] M. A. Akivis & V. Goldberg - "Differential geometry of webs", in Handbook of differential geometry, Vol. I, North-Holland, 2000, p. 1-152. | Zbl

[3] M. A. Akivis, V. Goldberg & V. Lychagin - "Linearizability of $d$ -webs, $d \geq 4$ , on two-dimensional manifolds", Selecta Math. (N.S.) 10 (2004), p. 431-451. | DOI | Zbl

[4] A. Beauville - "Géométrie des tissus [d'après S. S. Chern et P. A. Griffiths]", in Séminaire Bourbaki (1978/79), exp. n° 531, Lecture Notes in Math., vol. 770, Springer, 1980, p. 103-119. | DOI | EuDML | Numdam | Zbl

[5] W. Blaschke - "Über die Tangenten einer ebenen Kurve fünfter Klasse", Abh. Math. Semin. Hamb. Univ. 9 (1933), p. 313-317. | DOI | JFM | Zbl

[6] W. Blaschke & G. Bol - "Geométrie der Gewebe", Die Grundlehren der Math., vol. 49, Springer, 1938. | EuDML | JFM | Zbl

[7] G. Bol - "Flächengewebe im dreidimensionalen Raum", Abh. Math. Semin. Hamb. Univ. 10 (1934), p. 119-133. | JFM | Zbl

[8] G. Bol, "Über ein bemerkenswertes Fünfgewebe in der Ebene", Abh. Math. Semin. Hamb. Univ. 11 (1936), p. 387-393. | DOI | JFM | Zbl

[9] E. Bompiani & E. Di Bortolotti - "Ricerche sulle superficie dello spazio a cinque dimensioni e nuove caratterizzazioni delia superficie di Veronese", Math. Z. 42 (1937), p. 411-429. | DOI | EuDML | Zbl

[10] P. Buzano - "Determinazione e studio di superficie di $S_{5}$ le cui linee principali presentano una notevole particolarità", Ann. Mat. Pura Appl. 18 (1939), p. 51-76. | DOI | JFM

[11] P. Buzano, "Tipi notevoli di 5-tessuti di curve piane", Boll. Unione Mat. Ital. 1 (1939), p. 7-11. | JFM

[12] S. S. Chern - "Web geometry", Bull. Amer. Math. Soc. (N.S.)6 (1982), p. 1-8. | DOI | Zbl

[13] S. S. Chern, "Géométrie der gewebe", in Wilhelm Blaschke Gesammelte Werke. Band 5, Thales-Verlag, 1985, p. 25-27.

[14] S. S. Chern, "The mathematical works of Wilhelm Blaschke - an update", in Wilhelm Blaschke Gesammelte Werke. Band 5, Thales-Verlag, 1985, p. 21-23. | Zbl

[15] S. S. Chern & P. Griffiths -"Abel's theorem and webs", Jahresber. Deutsch. Math.-Verein. 80 (1978), p. 13-110. | EuDML | Zbl

[16] S. S. Chern & P. Griffiths, "An inequality for the rank of a web and webs of maximum rank", Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978), p. 539-557. | EuDML | Numdam | Zbl

[17] S. S. Chern & P. Griffiths, "Corrections and addenda to our paper: "Abel's theorem and webs"", Jahresber. Deutsch. Math.-Verein. 83 (1981), p. 78-83. | Zbl

[18] L. Chiantini & C. Ciliberto - "Weakly defective varieties", Trans. Amer. Math. Soc. 354 (2002), p. 151-178. | DOI | Zbl

[19] D. B. Damiano - "Webs and characteristic forms of Grassmann manifolds", Amer. J. Math. 105 (1983), p. 1325-1345. | DOI | Zbl

[20] F. Enriques - "Una questione sulla linearità dei sistemi di curve appartenenti ad una superficie algebrica", Rend. Acc. Lincei (1893), p. 3-8. | JFM

[21] V. Goldberg - "Rank problems for webs $W (d, 2, r)$ ", in Differential geometry and its applications (Eger, 1989), Colloq. Math. Soc. János Bolyai, vol. 56, North-Holland, 1992, p. 317-357. | Zbl

[22] V. Goldberg & V. Lychagin - "Abelian equations and rank problems for planar webs", preprint arXiv:math.DG/0605124, 2006. | Zbl

[23] V. Goldberg & V. Lychagin, "On the Blaschke conjecture for $3$ -webs", J. Geom. Anal. 16 (2006), p. 69-115. | DOI | Zbl

[24] P. Griffiths - "Variations on a theorem of Abel", Invent. Math. 35 (1976), p. 321-390. | DOI | EuDML | Zbl

[25] P. Griffiths, "The legacy of Abel in algebraic geometry", in The legacy of Niels Henrik Abel, Springer, 2004, p. 179-205. | DOI | Zbl

[26] J. Grifone, Z. Muzsnay & J. Saab - "On the linearizability of $3$ -webs", in Proceedings of the Third World Congress of Nonlinear Analysts, Part 4 (Catania, 2000), vol. 47, 2001, p. 2643-2654. | Zbl

[27] J. Grifone & E. Salem (eds.) - Web theory and related topics, World Scientific Publishing Co. Inc., 2001, papers from the Conférence on Webs held in Toulouse, December 1996. | Zbl

[28] A. Hénaut - "Sur la linéarisation des tissus de $𝐂^{2}$ ", Topology 32 (1993), p. 531-542. | DOI | Zbl

[29] A. Hénaut, "Sur l'algébrisation des tissus de codimension n de $𝐂^{2 n}$ ", Ann. Sci. Ecole Norm. Sup. (4) 31 (1998), p. 131-143. | DOI | EuDML | Numdam | MR | Zbl

[30] A. Hénaut, "Analytic web geometry", in Web theory and related topics (Toulouse, 1996), World Sci. Publ., River Edge, NJ, 2001, p. 6-47. | DOI | MR | Zbl

[31] A. Hénaut, "Formes différentielles abéliennes, bornes de Castelnuovo et géométrie des tissus", Comment Math. Helv. 79 (2004), p. 25-57. | DOI | MR | Zbl

[32] A. Hénaut, "On planar web geometry through abelian relations and connections", Ann. of Math. (2) 159 (2004), p. 425-445. | DOI | MR | Zbl

[33] A. Hénaut, "Planar web geometry through abelian relations and singularities", in Inspired by S. S. Chern, Nankai Tracts Math., vol. 11, World Sci. Publ., Hackensack, NJ, 2006, p. 269-295. | DOI | MR | Zbl

[34] G. Henkin & M. Passare - "Abelian differentials on singular varieties and variations on a theorem of Lie-Griffiths", Invent. Math. 135 (1999), p. 297-328. | DOI | MR | Zbl

[35] R. Macpherson - "The combinatorial formula of Gabrielov, Gel'fand and Losik for the first Pontrjagin class", in Séminaire Bourbaki (1976/77), exp. n° 497, Lecture Notes in Math., vol. 677, Springer, 1978, p. 105-124. | DOI | EuDML | Numdam | MR | Zbl

[36] D. Marin, J. V. Pereira & L. Pirio - "On planar webs with infinitésimal automorphisms", in Inspired by S. S. Chern, Nankai Tracts Math., vol. 11, World Sci. Publ., Hackensack, NJ, 2006, p. 351-364. | DOI | MR | Zbl

[37] N. N. Mihăileanu - "Sur les tissus plans de première espèce", Bull. Math. Soc. Roumaine Sci. 43 (1941), p. 23-26. | MR | Zbl

[38] I. Nakai - "Topology of complex webs of codimension one and geometry of projective space curves", Topology 26 (1987), p. 475-504. | DOI | MR | Zbl

[39] A. Pantazi - "Sur la détermination du rang d'un tissu plan", C. R. Acad. Sc. Roumanie 4 (1940), p. 108-111. | JFM

[40] L. Pirio - "Équations fonctionnelles abéliennes et géométrie des tissus", Ph.D. Thesis, Université Paris VI, 2004.

[41] L. Pirio, "Sur les tissus plans de rang maximal et le problème de Chern", C. R. Math. Acad. Sci. Paris 339 (2004), p. 131-136. | DOI | MR | Zbl

[42] L. Pirio, "Abelian functional équations, planar web geometry and polylogarithms", Selecta Math. (N.S.) 11 (2005), p. 453-489. | DOI | MR | Zbl

[43] L. Pirio & J.-M. Trépreau - "Tissus plans exceptionnels et fonctions thêta", Ann. Inst. Fourier (Grenoble) 55 (2005), p. 2209-2237. | DOI | EuDML | Numdam | MR | Zbl

[44] O. Ripoll - "Détermination du rang des tissus du plan et autres invariants géométriques", C. R. Math. Acad. Sci. Paris 341 (2005), p. 247-252. | DOI | MR | Zbl

[45] O. Ripoll, "Géométrie des tissus du plan et équations différentielles", Ph.D. Thesis, Université de Bordeaux I, 2005.

[46] O. Ripoll, "Properties of the connection associated with planar webs and applications", preprint arXiv:math.DG/0702321, 2007.

[47] G. Robert - "Relations fonctionnelles polylogarithmiques et tissus plans", 2002, preprint 146, Université de Bordeaux I.

[48] A. Terracini - "Su una possibile particolarità délie linee principali di una superficie. I i II", Atti Accad. Naz. Lincei 26 (1937), p. 84-91, 153-158. | JFM | Zbl

[49] J.-M. Trépreau - "Algébrisation des tissus de codimension 1. La généralisation d'un théorème de Bol", in Inspired by S. S. Chern, Nankai Tracts Math., vol. 11, World Sci. Publ., Hackensack, NJ, 2006, p. 399-433. | DOI | MR | Zbl

[50] W. Wirtinger - "Lies Translationsmannigfaltigkeiten und Abelsche Intégrale", Monatsh. Math. Phys. 46 (1938), p. 384-431. | DOI | MR | Zbl

[51] D. Zagier - "Polylogarithms, Dedekind zeta functions and the algebraic $K$ -theory of fields", in Arithmetic algebraic geometry (Texel, 1989), Progr. Math., vol. 89, Birkhäuser, 1991, p. 391-430. | DOI | MR | Zbl