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Regular homotopy of Hurwitz curves. (English. Russian original) Zbl 1071.14507

Izv. Math. 68, No. 3, 521-542 (2004); translation from Izv. Ross. Akad. Nauk Ser. Mat. 68, No. 3, 91-114 (2004).
Summary: We prove that any two irreducible cuspidal Hurwitz curves \(C_0\) and \(C_1\) (or, more generally, two curves with \(A\)-type singularities) in the Hirzebruch surface \({\mathbf F}_N\) with the same homology classes and sets of singularities are regular homotopic. Moreover, they are symplectically regular homotopic if \(C_0\) and \(C_1\) are symplectic with respect to a compatible symplectic form.

MSC:

14F35 Homotopy theory and fundamental groups in algebraic geometry
14H45 Special algebraic curves and curves of low genus
57R17 Symplectic and contact topology in high or arbitrary dimension
14H20 Singularities of curves, local rings
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