Geodesic
Poincaré Series of Divisorial Filtration Corresponding to a Curve with One Place at Infinity
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 60-68 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The exceptional divisor component of the projective plane modified by a sequence of blow-ups determines filtration on the ring of polynomials in two variables. The set of such components determines the multi-index filtration on this ring. The Poincaré series of this filtration is calculated for some sets of components provided that the modification under study is the minimal resolution of a plane algebraic curve with one place at infinity.
Keywords: plane irreducible affine curve, exceptional divisor, irreducible divisor, dual graph, complex projective plane.
Mots-clés : multi-index filtration, Poincaré series 
@article{MZM_2010_87_1_a6,
     author = {A. Yu. Buriyak},
     title = {Poincar\'e {Series} of {Divisorial} {Filtration} {Corresponding} to a {Curve} with {One} {Place} at {Infinity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {60--68},
     year = {2010},
     volume = {87},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a6/}
}
TY  - JOUR
AU  - A. Yu. Buriyak
TI  - Poincaré Series of Divisorial Filtration Corresponding to a Curve with One Place at Infinity
JO  - Matematičeskie zametki
PY  - 2010
SP  - 60
EP  - 68
VL  - 87
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a6/
LA  - ru
ID  - MZM_2010_87_1_a6
ER  - 
%0 Journal Article
%A A. Yu. Buriyak
%T Poincaré Series of Divisorial Filtration Corresponding to a Curve with One Place at Infinity
%J Matematičeskie zametki
%D 2010
%P 60-68
%V 87
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a6/
%G ru
%F MZM_2010_87_1_a6
A. Yu. Buriyak. Poincaré Series of Divisorial Filtration Corresponding to a Curve with One Place at Infinity. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 60-68. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a6/

[1] M. Suzuki, “Affine plane curves with one place at infinity”, Ann. Inst. Fourier (Grenoble), 49:2 (1999), 375–404 | MR | Zbl

[2] A. Campillo, F. Delgado, S. M. Gusein-Zade, “The Alexander polynomial of a plane curve singularity and integrals with respect to the Euler characteristic”, Internat. J. Math., 14:1 (2003), 47–54 | DOI | MR | Zbl

[3] M. Fujimoto, M. Suzuki, “Construction of affine plane curves with one place at infinity”, Osaka J. Math., 39:4 (2002), 1005–1027 | MR | Zbl

[4] A. Campillo, F. Delgado, S. M. Gusein-Zade, Multi-index filtrations corresponding to curves with one place at infinity and their Poincaré series, arXiv: math.AG/0506549v2

[5] H. Pinkham, Courbes planes ayant une seule place à l'infini, Preprint, Centre de Mathematiques de l'Ecole Polytechnique, Palaiseu, 1977/78