Regular homotopy of Hurwitz curves
Denis Auroux, Viktor S. Kulikov, Vsevolod V. Shevchishin
Abstract
We prove that any two irreducible cuspidal Hurwitz curves C0 and C1 (or more generally, curves with A-type singularities) in the Hirzebruch surface FN with coinciding homology classes and sets of singularities are regular homotopic; and symplectically regular homotopic if C0 and C1 are symplectic with respect to a compatible symplectic form.
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