On Poincaré series of filtrations

2015/04/19 by Campillo, A., Delgado, F., Gusein-Zade, S. M.
#13A18 #16W60 #16W70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.04849

Abstract

In this survey one discusses the notion of the Poincaré series of multi-index filtrations, an alternative approach to the definition, a method of computation of the Poincaré series based on the notion of integration with respect to the Euler characteristic (or rather on an infinite-dimensional version of it), generalizations of the notion of the multi-variable Poincaré series based on the notion of the motivic integration, and relations of the latter ones with some zeta functions over finite fields and with generating series of Heegaard-Floer homologies of algebraic links.

Related

• Multi-index filtrations and motivic Poincare series
• Multi-variable Poincaré series associated with Newton diagrams
• Poincare series of embedded filtrations
• An equivariant Poincaré series of filtrations and monodromy zeta functions
• Multi-index filtrations corresponding to curves with one place at infinity and their Poincaré series