For plane curve singularities, the paper characterizes which arcs map to vanishing cycles under the geometric variation operator, and constructs 'topological exceptional collections' of vanishing arcsets for any A'Campo divide.
Floer theory for the variation operator of an isolated singularity
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Vanishing arcs for isolated plane curve singularities
For plane curve singularities, the paper characterizes which arcs map to vanishing cycles under the geometric variation operator, and constructs 'topological exceptional collections' of vanishing arcsets for any A'Campo divide.