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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.

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