9 citations · 27 across the 20 of their papers we have counts for
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Poincaré series of valuations on functions over a field
Antonio Campillo, Felix Delgado, Sabir Gusein-Zade
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the co…
Real Poincaré series of a plane divisorial valuation
Antonio Campillo, Félix Delgado, Sabir M. Gusein-Zade
Earlier, there was computed the Poincaré series of a valuation or of a collection of valuations on the ring of germs of holomorphic functions in two variables. For a collection of…
On real analogues of the Poincaré series
A. Campillo, F. Delgado, S. M. Gusein-Zade
There exist several equivalent equations for the Poincaré series of a collection of valuations on the ring of germs of functions on a complex analytic variety. We give definitions…
Algebraic links in the Poincaré sphere and the Alexander polynomials
A. Campillo, F. Delgado, S. M. Gusein-Zade
The Alexander polynomial in several variables is defined for links in three-dimensional homology spheres, in particular, in the Poincaré sphere: the intersection of the surface $S=…
On the topological type of a set of plane valuations with symmetries
A. Campillo, F. Delgado, S. M. Gusein-Zade
Let be a set of irreducible plane curve singularities. For an action of a finite group , let be the Alexander polynomial in $r\vert…
Pencils and critical locus on normal surfaces
F. Delgado, H. Maugendre
We study linear pencils of curves on normal surface singularities. Using the minimal good resolution of the pencil, we describe the topological type of generic elements of the penc…
Equivariant Poincaré series and topology of valuations
A. Campillo, F. Delgado, S. M. Gusein-Zade
The equivariant with respect to a finite group action Poincaré series of a collection of valuations was defined earlier as a power series in variables with the coefficients…
On Poincaré series of filtrations
A. Campillo, F. Delgado, S. M. Gusein-Zade
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…
An equivariant Poincaré series of filtrations and monodromy zeta functions
A. Campillo, F. Delgado, S. M. Gusein-Zade
We define a new equivariant (with respect to a finite group action) version of the Poincaré series of a multi-index filtration as an element of the power series ring ${\widetil…
Hilbert function, generalized Poincaré series and topology of plane valuations
A. Campillo, F. Delgado, S. M. Gusein-Zade
To a multi-index filtration (say, on the ring of germs of functions on a germ of a complex analytic variety) one associates several invariants: the Hilbert function, the Poincaré s…
Equivariant Poincaré series of filtrations and topology
A. Campillo, F. Delgado, S. M. Gusein-Zade
Earlier, for an action of a finite group on a germ of an analytic variety, an equivariant -Poincaré series of a multi-index filtration in the ring of germs of functions on t…
Equivariant Poincare series of filtrations
A. Campillo, F. Delgado, S. M. Gusein-Zade
We offer a new approach to a definition of an equivariant version of the Poincaré series. This Poincaré series is defined not as a power series, but as an element of the Grothendie…
Poincare series of collections of plane valuations
A. Campillo, F. Delgado, S. M. Gusein-Zade +1
In earlier papers there were given formulae for the Poincare series of multi-index filtrations on the ring of germs of functions of two variables defined by collections of valuatio…
The Poincare series of divisorial valuations in the plane defines the topology of the set of divisors
A. Campillo, F. Delgado, S. M. Gusein-Zade
To a plane curve singularity one associates a multi-index filtration on the ring of germs of functions of two variables defined by the orders of a function on irreducible component…
Generating sequences and Poincaré series for a finite set of plane divisorial valuations
F. Delgado, C. Galindo, A. Núñez
Let be a finite set of divisorial valuations centered at a 2-dimensional regular local ring . In this paper we study its structure by means of the semigroup of values, …
Poincare series of filtrations corresponding to ideals on surfaces
A. Campillo, F. Delgado, S. M. Gusein-Zade
Earlier the authors considered and, in some cases, computed Poincare series of two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface…
Universal abelian covers of rational surface singularities and multi-index filtrations
A. Campillo, F. Delgado, S. M. Gusein-Zade
In previous papers, there were computed the Poincare series of some (multi-index) filtrations on the ring of germs of functions on a rational surface singularity. These Poincare se…
On Poincare series of filtrations on equivariant functions of two variables
A. Campillo, F. Delgado, S. M. Gusein-Zade
Let a finite group act on the complex plane . We consider multi-index filtrations on the spaces of germs of holomorphic functions of two variables equivariant…
Multi-index filtrations corresponding to curves with one place at infinity and their Poincaré series
A. Campillo, F. Delgado, S. M. Gusein-Zade
This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.
Multi-index filtrations and motivic Poincare series
Antonio Campillo, Felix Delgado, Sabir M. Gusein-Zade
The Poincare series of a multi-index filtration on the ring of germs of functions can be written as a certain integral with respect to the Euler characteristic over the projectiviz…