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Matematicheskie Zametki, 2010, Volume 87, Issue 1, Pages 60–68
DOI: https://doi.org/10.4213/mzm6380 (Mi mzm6380) 		 
Poincaré Series of Divisorial Filtration Corresponding to a Curve with One Place at Infinity

A. Yu. Buriyak

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm6380
Abstract: 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, multi-index filtration, exceptional divisor, Poincaré series, irreducible divisor, dual graph, complex projective plane.
Received: 21.08.2008
English version:
Mathematical Notes, 2010, Volume 87, Issue 1, Pages 52–58
DOI: https://doi.org/10.1134/S0001434610010074
Bibliographic databases:
UDC: 515.162
Language: Russian
Citation: A. Yu. Buriyak, “Poincaré Series of Divisorial Filtration Corresponding to a Curve with One Place at Infinity”, Mat. Zametki, 87:1 (2010), 60–68; Math. Notes, 87:1 (2010), 52–58
Citation in format AMSBIB
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