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On resolution complexity of plane curves. (English) Zbl 0844.14010
The authors show that any isolated plane curve singular point can be resolved in a sequence of toroidal blowing-ups. They prove that the minimal number of required toroidal blowing-ups is a topological invariant depending on the number of local branches and number of Puiseux pairs of each branch. That minimal number is called resolution complexity. – The behavior of the resolution complexity for singular points of hypersurfaces and its connection with complexity of plane sections are stated as open problems.

MSC:
14H20 Singularities of curves, local rings
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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