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math.AG2008★ 1 cited
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…
math.AG2008
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, …
math.AG2008
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…