9 citations · 27 across the 20 of their papers we have counts for
20 papers
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…