The present article aims to discuss the graded roots introduced by the author in his study of
the topology of normal surface singularities. In the body of the paper we emphasize two …

It is a very old and interesting open problem to characterize those collections of embedded
topological types of local plane curve singularities which may appear as singularities of a …

Abstract Let E⊆ P 2 be a complex rational cuspidal curve contained in the projective plane.
The Coolidge–Nagata conjecture asserts that E is Cremona-equivalent to a line, that is, it is …

We show a counterexample to a conjecture of de Bobadilla, Luengo, Melle-Hern\'{a} ndez
and N\'{e} methi on rational cuspidal projective plane curves. The counterexample is a …

Submission on request. This Master thesis from 2008 (University of Oslo, Norway) contains
no new results, but it provides an overview of plane rational cuspidal curves, in particular …

We construct the analytic lattice cohomology associated with the analytic type of any
complex normal surface singularity. It is the categorification of the geometric genus of the …

To classify planar complex rational cuspidal curves E⊆ P 2 it remains to classify the ones
with complement of log general type, that is, the ones for which κ (KX+ D)= 2, where (X, D) is …

Abstract Let E⊆ ℙ 2 be a complex rational cuspidal curve and let (X, D)→(ℙ 2, E) be the
minimal log resolution of singularities. We prove that E has at most six cusps and we …

Using the path lattice cohomology we provide a conceptual topological characterization of
the geometric genus for certain complex normal surface singularities with rational homology …

Complex planar curves homeomorphic to a line have at most four singular points -
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