Poincaré series on good semigroup ideals

2018/09/03 by Tozzo, Laura
#05E05 #06F05 #14H20 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.00583

Abstract

The Poincaré series of a ring associated to a plane curve was defined by Campillo, Delgado, and Gusein-Zade. This series, defined through the value semigroup of the curve, encodes the topological information of the curve. In this paper we extend the definition of Poincaré series to the class of good semigroup ideals, to which value semigroups of curves belong. Using this definition we generalize a result of Pol: under suitable assumptions, given good semigroup ideals E and K, with K canonical, the Poincaré series of K-E is symmetric to the Poincaré series of E.

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