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Título
Integration over the space of functions and Poincar´e series: a revision
Año del Documento
2018
Editorial
Springer
Descripción
Producción Científica
Documento Fuente
Proceedings of the Steklov Institute of Mathematics, 2018, vol. 302, p. 1-15
Resumen
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.
Palabras Clave
Filtrations
Filtraciones
Plane valuation
Valoración de aviones
Poincaré series
Serie de Poincaré
ISSN
1531-8605
Revisión por pares
SI
Patrocinador
Ministerio de Economía, Industria y Competitividad (MTM2015-65764-C3-1-P)
Russian Science Foundation (grant 16-11- 10018)
Russian Science Foundation (grant 16-11- 10018)
Version del Editor
Propietario de los Derechos
© 2018 Springer
Idioma
eng
Derechos
openAccess
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