Интегрирование По Эйлеровой Характеристике По Пространству Функций И Полином Александера Особенности Плоской Кривой

In [1] and [2], there were computed the Poincaré series of some (multi-index) filtrations on the ring of germs of functions on a rational surface singularity. These Poincaré series were written as the integer parts of certain fractional power series, an interpretation of whom was not given. Here we show that, up to a simple change of variables, these fractional power series are specializations of the equivariant Poincaré series for filtrations on the ring Ø e S,0 of germs of functions on the universal abelian cover ( S, 0) of the surface (S, 0). We compute these equivariant Poincaré series. From another point of view universal abelian covers of rational surface singularities were studied in [6].Let (S, 0) be an isolated complex rational surface singularity and let π : (X, D) → (S, 0) be a resolution of it (not necessarily the minimal one). Here X is a smooth complex surface, the exceptional divisor D = π −1 (0) is a normal crossing divisor on X, all components E σ (σ ∈ Γ) of the exceptional divisor D are isomorphic to the complex projective line CP 1 and the dual graph of the resolution is a tree.

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Universal Abelian covers of rational surface singularities and multi-index filtrations

Guseĭn-Zade

Delgado

Campillo

2008

Funct Anal Its Appl

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Integration with respect to the Euler characteristic and its applications

Guseĭn-Zade¹

2010

Uspekhi Mat. Nauk

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Обсуждается понятие интегрирования по эйлеровой характеристике и его обобщения: интегрирование по бесконечномерным пространствам дуг или функций, мотивное интегрирование. Описываются приложения этих понятий к вычислению дзета-функций монодромий, рядов Пуанкаре мультииндексных фильтраций, производящих рядов классов некоторых классифицирующих пространств и т. д. Библиография: 70 названий.

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Интегрирование По Эйлеровой Характеристике По Пространству Функций И Полином Александера Особенности Плоской Кривой

Cited by 2 publications

References 2 publications

Universal Abelian covers of rational surface singularities and multi-index filtrations

Universal Abelian covers of rational surface singularities and multi-index filtrations

Integration with respect to the Euler characteristic and its applications

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