Tropical and algebraic curves with multiple points

Details Tropical and algebraic curves with multiple points Tropical and algebraic curves with multiple points

2009-04-18

arxiv.org/abs/0904.2834v2

Mathematics

Algebraic Geometry

35 pages, 3 figures, numerous corrections are made, few illustrating examples are added

Scientific paper

Patchworking theorems serve as a basic element of the correspondence between tropical and algebraic curves, which is a core of the tropical enumerative geometry. We present a new version of a patchworking theorem which relates plane tropical curves with complex and real algebraic curves having prescribed multiple points. It can be used to compute Welschinger invariants of non-toric Del Pezzo surfaces.

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