Discuterò una costruzione geometrica, fatta insieme a De Concini, di una modificazione di una configurazione di sottospazi che trasforma i sottospazi in un divisore a incroci normali. Inoltre nel caso di iperpiani questa costruzione è legata alla generalizzazione della equazione di Kniznik-Zamolodchikov ed alla teoria dei nodi, per i sistemi di radici produce dei modelli particolarmente interessati.
I shall discuss a geometric construction, done with De Concini, of a blowup of a configuration of subspaces making it into a divisor with normal crossings. For hyperplanes this is related to a generalization of the Khiznik-Zamolodchikov equation and to knot theory. For root systems this produces a particularly interesting model.
@article{RLIN_1996_9_7_2_113_0,
author = {Claudio Procesi},
title = {Complementi di sottospazi e singolarit\`a coniche},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {7},
year = {1996},
pages = {113-123},
zbl = {0891.14014},
mrnumber = {1438609},
language = {it},
url = {http://dml.mathdoc.fr/item/RLIN_1996_9_7_2_113_0}
}
Procesi, Claudio. Complementi di sottospazi e singolarità coniche. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 7 (1996) pp. 113-123. http://gdmltest.u-ga.fr/item/RLIN_1996_9_7_2_113_0/
[1] , Functions hyperlogarithmiques et groupes de monodromie unipotents. J. Fac. Univ. Tokyo, 25, 1978, 149-156. | MR 509582 | Zbl 0416.32020
[2] , The Vassiliev theory of discriminants and knots. In: First European Congress of Mathematics. Birkhäuser, Basel1994. | MR 1341819 | Zbl 0869.57006
[3] , Non associative tangles. Harvard1993, preprint. | MR 1470726 | Zbl 0888.57008
[4] , On the Vassiliev knot invariants. Topology, 34, 1995, 423-472. | MR 1318886 | Zbl 0898.57001
[5] , Groupes et algèbres de Lie Ch. 4-5-6. Hermann, Paris1981. | Zbl 0483.22001
[6] , Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe. Inv. Math., 12, 1971, 57-61. | MR 293615 | Zbl 0204.56502
[7] , Sur les groupes de tresses (d'après V. I. Arnold). Séminaire Bourbaki 1971/72, S.L.N., 317, 1973. | MR 422674 | Zbl 0277.55003
[8] , Construction combinatoire des invariants de Vassiliev-Kontsevich des noeuds. C.R. Acad. Sci. Paris, Sér. I Math., 316, 1993, 1205-1210. | MR 1221650 | Zbl 0791.57006
[9] , Iterated integrals of differential forms and loop space cohomology. Ann. of Math., 1973, 217-246. | MR 380859 | Zbl 0227.58003
[10] , Generalized Braid Groups and local r-matrix systems. Doklady Akad. Nauk SSSR, 307, 1989, 27-34. | MR 1017085 | Zbl 0747.17017
[11] , Monodromy representations for generalized Knizhnik-Zamolodchikov equations and Hecke algebras. Publ. RIMS, Kyoto Univ., 27, 1991, 711-726. | MR 1143033 | Zbl 0753.17035
[12] - , Wonderful models of subspace arrangements. Selecta Mathematica, 1, 1995, 459-494. | MR 1366622 | Zbl 0842.14038
[13] - , Hyperplane arrangements and holonomy equations. Selecta Mathematica, 1, 1995, 495-535. | MR 1366623 | Zbl 0848.18004
[14] , Les immeubles de groupes de tresses généralisés. Invent. Math., 17, 1972, 273-302. | MR 422673 | Zbl 0238.20034
[15] , Le groupe fondamental de la droite projective moins trois points. In: Galois groups over . Ed. , , , Publ. M.S.R.L., 16, 1987, 79-298. | MR 1012168 | Zbl 0742.14022
[16] , Quasi Hopf algebras. Leningrad Math. J., 1, 1990, 1419-1457. | MR 1047964
[17] , On quasi triangular quasi-Hopf algebras and a group closely connected with . Leningrad Math. J., 2, 1991, 829-860. | MR 1080203 | Zbl 0728.16021
[18] , Reflection groups and Coxeter groups. Cambridge Studies in Adv. Math., 29, 1992. | Zbl 0768.20016
[19] , The permutoassociahedron, Mac Lane's coherence theorem and asymptotic zones for the KZ equation. J. Pure and Appl. Alg., 85, 1993, 119-142. | MR 1207505 | Zbl 0812.18003
[20] , Quantum Groups. Graduate Texts in Math.Springer, 155, 1995. | MR 1321145 | Zbl 0808.17003
[21] , Intersection theory of moduli space of stable N-pointed curves of genus 0. T.A.M.S., 330, 1992, 545-574. | MR 1034665 | Zbl 0768.14002
[22] , On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces. Nagoya Math. J., 93, 1983, 21-37. | MR 726138 | Zbl 0503.57001
[23] , Monodromy representations of braid groups and Yang-Baxter equations. Ann. Inst. Fourier, 37, 1987, 139-160. | MR 927394 | Zbl 0634.58040
[24] - , Current algebra and the Wess-Zumino model in two dimensions. Soviet J. on Nuclear Physics, 247, 1984, 83-103. | MR 853258 | Zbl 0661.17020
[25] , Vassilev's knot invariant. Advances in Soviet Math., 16, 1993, 137-150. | MR 1237836 | Zbl 0839.57006
[26] - , Representations of the category of tangles by Kontsevich's iterated integral. Max-Planck-Institut Bonn, preprint. | Zbl 0839.57008
[27] , Combinatorial expression for universal Vassilev's link invariant. Harvard Univ.1993, preprint. | MR 1324388 | Zbl 0996.57501
[28] , Complements of discriminants of smooth maps. A.M.S. Transl., 98, 1992. | Zbl 0762.55001