Regular homotopy of Hurwitz curves

Details Regular homotopy of Hurwitz curves Regular homotopy of Hurwitz curves

2004-01-14

arxiv.org/abs/math/0401172v1

Mathematics

Symplectic Geometry

26 pages

Scientific paper

We prove that any two irreducible cuspidal Hurwitz curves $C_0$ and $C_1$ (or
more generally, curves with A-type singularities) in the Hirzebruch surface
$F_N$ with coinciding homology classes and sets of singularities are regular
homotopic; and symplectically regular homotopic if $C_0$ and $C_1$ are
symplectic with respect to a compatible symplectic form.

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