dc.contributor.author | Campillo López, Antonio | |
dc.contributor.author | Delgado de la Mata, Félix | |
dc.contributor.author | Gusein-Zade, Sabir M. | |
dc.date.accessioned | 2019-05-06T11:23:44Z | |
dc.date.available | 2019-05-06T11:23:44Z | |
dc.date.issued | 2018 | |
dc.identifier.citation | Proceedings of the Steklov Institute of Mathematics, 2018, vol. 302, p. 1-15 | es |
dc.identifier.issn | 1531-8605 | es |
dc.identifier.uri | http://uvadoc.uva.es/handle/10324/35937 | |
dc.description | Producción Científica | es |
dc.description.abstract | Earlier (2000) the authors introduced the notion of the integral with
respect to the Euler characteristic over the space of germs of functions on
a variety and over its projectivization. This notion permitted to rewrite
in new terms known definitions and statements and also appeared to be
an effective tool to compute Poincar´e series of multi-index filtrations in
some situations. However the “classical” (initial) notion can be applied
only to multi-index filtrations defined by so-called finitely determined
valuations (or order functions). Here we introduce a modified version of
the notion of the integral with respect to the Euler characteristic over
the projectivization of the space of function germs. This version can be
applied in a number of settings where the “classical approach” does not
work. We give examples of application of this concept for definitions
and computations of the Poincar´e series of collections of plane valuations
which include valuations not centred at the origin, including equivariant
ones. | es |
dc.format.mimetype | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Springer | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.subject.classification | Filtrations | es |
dc.subject.classification | Filtraciones | es |
dc.subject.classification | Plane valuation | es |
dc.subject.classification | Valoración de aviones | es |
dc.subject.classification | Poincaré series | es |
dc.subject.classification | Serie de Poincaré | es |
dc.title | Integration over the space of functions and Poincar´e series: a revision | es |
dc.type | info:eu-repo/semantics/article | es |
dc.rights.holder | © 2018 Springer | es |
dc.identifier.doi | 10.1134/S008154381806007X | es |
dc.relation.publisherversion | https://link.springer.com/article/10.1134/S008154381806007X#Bib1 | es |
dc.peerreviewed | SI | es |
dc.description.project | Ministerio de Economía, Industria y Competitividad (MTM2015-65764-C3-1-P) | es |
dc.description.project | Russian Science Foundation (grant 16-11- 10018) | es |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | |