The Coolidge-Nagata conjecture holds for curves with more than four cusps

Details The Coolidge-Nagata conjecture holds for curves with more than four cusps The Coolidge-Nagata conjecture holds for curves with more than four cusps

2012-02-16

arxiv.org/abs/1202.3491v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

Let E be a plane rational curve defined over complex numbers which has only locally irreducible singularities. The Coolidge-Nagata conjecture states that E is rectifiable, i.e. it can be transformed into a line by a birational automorphism of the plane. We show that if it is not rectifiable then the tree of the exceptional divisor for its minimal embedded resolution of singularities has at most nine maximal twigs. This settles the conjecture in case E has more than four singular points.

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