Geodesic
Poincar\'e Series of Divisorial Filtration Corresponding to a Curve with One Place at Infinity
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 60-68

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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, Poincaré series, irreducible divisor, dual graph, complex projective plane.
Mots-clés : multi-index filtration 
@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},
     publisher = {mathdoc},
     volume = {87},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a6/}
}
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A. Yu. Buriyak. Poincar\'e 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/