Three Dimensional Saito Free Divisors and Singular Curves
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 1, pp. 33-41.

Voir la notice de l'article provenant de la source Math-Net.Ru

The purpose of the present study is to find out examples of Saito free divisors by constructing Lie algebras generated by logarithmic vector fields along them. In the course of the study, the author recognized a deep connection between Saito free divisors and deformations of curve singularities. In this paper, we will explain a method of constructing three dimensional Saito free divisors and show some examples.
@article{JSFU_2008_1_1_a3,
     author = {Jiro Sekiguchi},
     title = {Three {Dimensional} {Saito} {Free} {Divisors} and {Singular} {Curves}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {33--41},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a3/}
}
TY  - JOUR
AU  - Jiro Sekiguchi
TI  - Three Dimensional Saito Free Divisors and Singular Curves
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2008
SP  - 33
EP  - 41
VL  - 1
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a3/
LA  - en
ID  - JSFU_2008_1_1_a3
ER  - 
%0 Journal Article
%A Jiro Sekiguchi
%T Three Dimensional Saito Free Divisors and Singular Curves
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2008
%P 33-41
%V 1
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a3/
%G en
%F JSFU_2008_1_1_a3
Jiro Sekiguchi. Three Dimensional Saito Free Divisors and Singular Curves. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 1, pp. 33-41. http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a3/

[1] A. G. Aleksandrov, “Nonisolated hypersurfaces singularities”, Advances in Soviet Math., 1 (1990), 211–246 | MR | Zbl

[2] A. G. Aleksandrov, “Moduli of logarithmic connections along free divisor”, Contemp. Math., 314 (2002), 2–23 | MR | Zbl

[3] A. G. Aleksandrov, J. Sekiguchi, “Free deformations of hypersurface singularities”, RIMS Kokyuroku (to appear)

[4] V. Arnol'd, “Normal forms of functions in the neighbourhoods of degenerate critical points”, Russian Math. Surveys, 29 (1976), 10–50 | DOI | MR

[5] V. Arnol'd, “Local normal forms of functions”, Invent. Math., 35 (1976), 87–109 | DOI | MR | Zbl

[6] N. Bourbaki, Groupes et Algèbres de Lie, Chaps. 4, 5, 6, Herman, Paris, 1968 | MR

[7] J. Damon, “On the freeness of equisingular deformations of plane curve singularities”, Topology Appl., 118:1–2 (2002), 31–43 | DOI | MR | Zbl

[8] W. Ebeling, “Quadratische Formen und Monodromiegruppen von Singularitäten”, Math. Ann., 255 (1981), 463–498 | DOI | MR | Zbl

[9] A. M. Gabrielov, “Dynkin diagrams for unimodular singularities”, Funct. Anal. Appl., 8 (1974), 192–196 | DOI | MR | Zbl

[10] M. Granger, D. Mond, A. N. Reyes, M. Schulze, Linear free divisors, preprint

[11] T. Ishibe, Master thesis presented to RIMS, Kyoto University, 2007

[12] K. Saito, “Theory of logarithmic differential forms and logarithmic vector fields”, J. Faculty of Sciences, Univ. Tokyo, Sect. IA Math., 27 (1980), 265–291 | MR | Zbl

[13] J. Sekiguchi, “Some topics related with discriminant polynomials”, RIMS Kokyuroku, 810 (1992), 85–94 | MR | Zbl

[14] J. Sekiguchi, A classification of weighted homogeneous Saito free divisors in three dimensional space, Preprint

[15] J. Sekiguchi, “Three dimensional Saito free divisors and deformations of singular curves”, RIMS Kokyuroku (to appear)

[16] P. Slodowy, Simple Singularities and Simple Algebraic Groups, Springer LNM, 815 | MR | Zbl

[17] H. Terao, “Arrangements of hyperplanes and their freeness, I, II”, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 27 (1980), 293–320 | MR

[18] T. Urabe, “Dynkin graphs, Gabrielov graphs, and triangular singularities”, J. Math. Sciences, 82 (1996), 3721–3729 | DOI | MR | Zbl

[19] T. Yano, J. Sekiguchi, “The microlocal structure of weighted homogeneous polynomials associated with Coxeter systems. I”, Tokyo J. Math., 2 (1979), 193–219 | MR | Zbl

[20] T. Yano, J. Sekiguchi, “The microlocal structure of weighted homogeneous polynomials associated with Coxeter systems. II”, Tokyo J. Math., 4 (1981), 1–34 | MR | Zbl