5 papers
Real morsifications via the trace map
Pablo Portilla Cuadrado
We prove that every reduced real plane curve singularity admits a real morsification. This settles a question of A'Campo and Gusein-Zade, later stated as conjectures by Leviant--Sh…
On the integral variation map of isolated plane curves singularities
Pablo Portilla Cuadrado, Baldur Sigurðsson
The integral variation map and algebraic monodromy of isolated plane curve singularities are important homological invariants of the singularity which are still far from being comp…
The total spine of the Milnor fibration of a plane curve singularity
Pablo Portilla Cuadrado, Baldur Sigurðsson
For any plane curve singularity defined by an analytic function germ , we construct a spine on each Milnor fiber simultaneously, that realizes the vanishing topology. In order t…
Vanishing arcs for isolated plane curve singularities
Hanwool Bae, Cheol-Hyun Cho, Dongwook Choa +2
The variation operator associated with an isolated hypersurface singularity is a classical topological invariant that relates relative and absolute homologies of the Milnor fiber v…
Plane curve singularities via divides
Norbert A'Campo, Pablo Portilla Cuadrado
Generic relative immersions of compact one-manifolds in the closed unit disk, i.e. divides, provide a powerful combinatorial framework, and allow a topological construction of fibe…