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math.AG2004★ 1 cited
On rational cuspidal projective plane curves
J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández +1
In the open problem of classification of rational cuspidal plane curves it is essential to find good necessary conditions on the type of singularities of a curve C in order C to ex…
math.AG2003
Relative Morsification Theory
Javier Fernandez de Bobadilla
In this paper we develope a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously kno…
math.AG2002
Topological finite-determinacy of functions with non-isolated singularities
J. Fernandez de Bobadilla
We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal , which provides a notion of topological finite-determinacy of fu…