On a class of local systems associated to plane curves
[Sur une classe de systèmes locaux associés aux courbes planes]
Silva, Pedro C.1
1 CMAF, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 421-426.

On étudie une classe de systèmes locaux sur le complément d'un germe de courbe irréductible plane. On présente des systèmes locaux qui par [8] correspondent à des 𝒟-modules holonomes réguliers dont la variété caractéristique est l'union de la section nulle avec le conormal de la courbe.

We study a class of local systems on the complement of a germ of irreducible plane curve. We exhibit local systems which by [8] give rise to regular holonomic 𝒟-modules with characteristic variety the union of the zero section with the conormal of the curve.

Reçu le :
Révisé le :
Publié le :
DOI : 10.1016/S1631-073X(02)02516-5
Silva, Pedro C. 1

1 CMAF, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal 
@article{CRMATH_2002__335_5_421_0,
     author = {Silva, Pedro C.},
     title = {On a class of local systems associated to plane curves},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {421--426},
     publisher = {Elsevier},
     volume = {335},
     number = {5},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02516-5},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02516-5/}
}
TY  - JOUR
AU  - Silva, Pedro C.
TI  - On a class of local systems associated to plane curves
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 421
EP  - 426
VL  - 335
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(02)02516-5/
DO  - 10.1016/S1631-073X(02)02516-5
LA  - en
ID  - CRMATH_2002__335_5_421_0
ER  - 
%0 Journal Article
%A Silva, Pedro C.
%T On a class of local systems associated to plane curves
%J Comptes Rendus. Mathématique
%D 2002
%P 421-426
%V 335
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02516-5/
%R 10.1016/S1631-073X(02)02516-5
%G en
%F CRMATH_2002__335_5_421_0
Silva, Pedro C. On a class of local systems associated to plane curves. Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 421-426. doi : 10.1016/S1631-073X(02)02516-5. http://www.numdam.org/articles/10.1016/S1631-073X(02)02516-5/

[1] A. Dimca, A. Némethi, On the monodromy of complex polynomials, | arXiv

[2] Formanek, E. Braid group representations of low degree, Proc. London Math. Soc., Volume 73 (1996) no. 3, pp. 279-322

[3] Galligo, A.; Granger, M.; Maisonobe, Ph. 𝒟-Modules et faisceaux pervers dont le support singulier est un croisement normal, Ann. Inst. Fourier, Volume 35 (1985), pp. 1-48

[4] Kashiwara, M. The Riemann–Hilbert problem for holonomic systems, Publ. Res. Inst. Math. Sci., Volume 20 (1984), pp. 319-365

[5] Kohno, M. Global Analysis in Linear Differential Equations, Kluwer Academic, 1999

[6] Mebkhout, Z. Une équivalence de catégories, Comput. Math., Volume 51 (1984), pp. 51-62

[7] Mebkhout, Z. Une autre équivalence de catégories, Comput. Math., Volume 51 (1984), pp. 63-88

[8] Neto, O. A microlocal Riemann–Hilbert correspondence, Comput. Math., Volume 127 (2001), pp. 229-241

[9] Neto, O.; Silva, P.C. Holonomic Systems with solutions ramified along a cusp, C. R. Acad. Sci. Paris, Série I, Volume 335 (2002), pp. 171-176

[10] Zariski, O. On the topology of algebroid singularities, Amer. J. Math., Volume 54 (1932), pp. 453-465

Cité par Sources :