RT info:eu-repo/semantics/article
T1 Integration over the space of functions and Poincar´e series: a revision
A1 Campillo López, Antonio
A1 Delgado de la Mata, Félix
A1 Gusein-Zade, Sabir M.
K1 Filtrations
K1 Filtraciones
K1 Plane valuation
K1 Valoración de aviones
K1 Poincaré series
K1 Serie de Poincaré
AB Earlier (2000) the authors introduced the notion of the integral withrespect to the Euler characteristic over the space of germs of functions ona variety and over its projectivization. This notion permitted to rewritein new terms known definitions and statements and also appeared to bean effective tool to compute Poincar´e series of multi-index filtrations insome situations. However the “classical” (initial) notion can be appliedonly to multi-index filtrations defined by so-called finitely determinedvaluations (or order functions). Here we introduce a modified version ofthe notion of the integral with respect to the Euler characteristic overthe projectivization of the space of function germs. This version can beapplied in a number of settings where the “classical approach” does notwork. We give examples of application of this concept for definitionsand computations of the Poincar´e series of collections of plane valuationswhich include valuations not centred at the origin, including equivariantones.
PB Springer
SN 1531-8605
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/35937
UL http://uvadoc.uva.es/handle/10324/35937
LA eng
NO Proceedings of the Steklov Institute of Mathematics, 2018, vol. 302, p. 1-15
NO Producción Científica
DS UVaDOC
RD 16-jul-2024