Algebraization of codimension one webs [after Trépreau, Hénaut, Pirio, Robert, ...]
Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque no. 317  (2008), Talk no. 974, p. 243-268
@incollection{AST_2008__317__243_0,
     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},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {317},
     year = {2008},
     note = {talk:974},
     pages = {243-268},
     zbl = {1184.14014},
     language = {en},
     url = {http://www.numdam.org/item/AST_2008__317__243_0}
}
Pereira, Jorge Vitório. Algebraization of codimension one webs [after Trépreau, Hénaut, Pirio, Robert, ...], in Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981, Astérisque, no. 317 (2008), Talk no. 974, pp. 243-268. http://www.numdam.org/item/AST_2008__317__243_0/

[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 0968.53001

[3] M. A. Akivis, V. Goldberg & V. Lychagin - "Linearizability of d-webs, d4, on two-dimensional manifolds", Selecta Math. (N.S.) 10 (2004), p. 431-451. | Article | Zbl 1073.53021

[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. | Article | Numdam | Zbl 0436.57008

[5] W. Blaschke - "Über die Tangenten einer ebenen Kurve fünfter Klasse", Abh. Math. Semin. Hamb. Univ. 9 (1933), p. 313-317. | Article | JFM 59.1377.03 | Zbl 0007.07804

[6] W. Blaschke & G. Bol - "Geométrie der Gewebe", Die Grundlehren der Math., vol. 49, Springer, 1938. | JFM 64.0727.03 | Zbl 0020.06701

[7] G. Bol - "Flächengewebe im dreidimensionalen Raum", Abh. Math. Semin. Hamb. Univ. 10 (1934), p. 119-133. | JFM 60.0628.01 | Zbl 0009.18105

[8] G. Bol, "Über ein bemerkenswertes Fünfgewebe in der Ebene", Abh. Math. Semin. Hamb. Univ. 11 (1936), p. 387-393. | Article | JFM 62.0830.01 | Zbl 0014.23005

[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. | Article | Zbl 0016.07401

[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. | Article | JFM 65.0819.01

[11] P. Buzano, "Tipi notevoli di 5-tessuti di curve piane", Boll. Unione Mat. Ital. 1 (1939), p. 7-11. | JFM 65.0818.03

[12] S. S. Chern - "Web geometry", Bull. Amer. Math. Soc. (N.S.)6 (1982), p. 1-8. | Article | Zbl 0483.53013

[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 0264.01021

[15] S. S. Chern & P. Griffiths -"Abel's theorem and webs", Jahresber. Deutsch. Math.-Verein. 80 (1978), p. 13-110. | Zbl 0386.14002

[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. | Numdam | Zbl 0402.57001

[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 0474.14003

[18] L. Chiantini & C. Ciliberto - "Weakly defective varieties", Trans. Amer. Math. Soc. 354 (2002), p. 151-178. | Article | Zbl 1045.14022

[19] D. B. Damiano - "Webs and characteristic forms of Grassmann manifolds", Amer. J. Math. 105 (1983), p. 1325-1345. | Article | Zbl 0528.53022

[20] F. Enriques - "Una questione sulla linearità dei sistemi di curve appartenenti ad una superficie algebrica", Rend. Acc. Lincei (1893), p. 3-8. | JFM 25.1215.01

[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 0789.53008

[22] V. Goldberg & V. Lychagin - "Abelian equations and rank problems for planar webs", preprint arXiv:math.DG/0605124, 2006. | Zbl 1298.53016

[23] V. Goldberg & V. Lychagin, "On the Blaschke conjecture for 3-webs", J. Geom. Anal. 16 (2006), p. 69-115. | Article | Zbl 1104.53011

[24] P. Griffiths - "Variations on a theorem of Abel", Invent. Math. 35 (1976), p. 321-390. | Article | Zbl 0339.14003

[25] P. Griffiths, "The legacy of Abel in algebraic geometry", in The legacy of Niels Henrik Abel, Springer, 2004, p. 179-205. | Article | Zbl 1072.14001

[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 1042.93526

[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 0983.00024

[28] A. Hénaut - "Sur la linéarisation des tissus de 𝐂 2 ", Topology 32 (1993), p. 531-542. | Article | Zbl 0799.32010

[29] A. Hénaut, "Sur l'algébrisation des tissus de codimension n de 𝐂 2n ", Ann. Sci. Ecole Norm. Sup. (4) 31 (1998), p. 131-143. | Article | Numdam | MR 1604302 | Zbl 0906.53007

[30] A. Hénaut, "Analytic web geometry", in Web theory and related topics (Toulouse, 1996), World Sci. Publ., River Edge, NJ, 2001, p. 6-47. | Article | MR 1837882 | Zbl 1011.53013

[31] A. Hénaut, "Formes différentielles abéliennes, bornes de Castelnuovo et géométrie des tissus", Comment Math. Helv. 79 (2004), p. 25-57. | Article | MR 2031299 | Zbl 1064.53011

[32] A. Hénaut, "On planar web geometry through abelian relations and connections", Ann. of Math. (2) 159 (2004), p. 425-445. | Article | MR 2052360 | Zbl 1069.53020

[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. | Article | MR 2313337 | Zbl 1133.53012

[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. | Article | MR 1666771 | Zbl 0932.32012

[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. | Article | Numdam | MR 521763 | Zbl 0388.57013

[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. | Article | MR 2313341 | Zbl 1129.14016

[37] N. N. Mihăileanu - "Sur les tissus plans de première espèce", Bull. Math. Soc. Roumaine Sci. 43 (1941), p. 23-26. | MR 12503 | Zbl 0063.03932

[38] I. Nakai - "Topology of complex webs of codimension one and geometry of projective space curves", Topology 26 (1987), p. 475-504. | Article | MR 919731 | Zbl 0647.57018

[39] A. Pantazi - "Sur la détermination du rang d'un tissu plan", C. R. Acad. Sc. Roumanie 4 (1940), p. 108-111. | JFM 64.0727.01

[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. | Article | MR 2078303 | Zbl 1065.53018

[42] L. Pirio, "Abelian functional équations, planar web geometry and polylogarithms", Selecta Math. (N.S.) 11 (2005), p. 453-489. | Article | MR 2215261 | Zbl 1109.39023

[43] L. Pirio & J.-M. Trépreau - "Tissus plans exceptionnels et fonctions thêta", Ann. Inst. Fourier (Grenoble) 55 (2005), p. 2209-2237. | Article | Numdam | MR 2207382 | Zbl 1090.53020

[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. | Article | MR 2164681 | Zbl 1088.53006

[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 63.0684.03 | Zbl 0017.22602

[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. | Article | MR 2313344 | Zbl 1136.53010

[50] W. Wirtinger - "Lies Translationsmannigfaltigkeiten und Abelsche Intégrale", Monatsh. Math. Phys. 46 (1938), p. 384-431. | Article | MR 1550755 | Zbl 0019.18204

[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. | Article | MR 1085270 | Zbl 0728.11062