Geodesic
Regular homotopy of Hurwitz curves
Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 521-542.

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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 $\boldsymbol F_N$ 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. 
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Vik. S. Kulikov; D. Auroux; V. V. Shevchishin. Regular homotopy of Hurwitz curves. Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 521-542. http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a5/

[1] Barraud J.-F., Courbes pseudo-holomorphes équisingulières en dimension 4, Ph. D. Thesis, Toulouse, 1998; Bull. Soc. Math. France, 128 (2000), 179–206 | MR | Zbl

[2] Barraud J.-F., “Nodal symplectic spheres in $\mathbb{CP}^2$ with positive self-intersection”, Internat. Math. Res. Notices, 1999, no. 9, 495–508 | DOI | MR | Zbl

[3] Hofer H., Lizan V., Sikorav J.-C., “On genericity for holomorphic curves in four-dimensional almost-complex manifolds”, J. of Geom. Anal., 7 (1998), 149–159 | MR

[4] Ivashkovich S. M., Shevchishin V. V., “Deformatsii nekompaktnykh kompleksnykh krivykh i obolochki meromorfnosti sfer”, Matem. sb., 189:9 (1998), 23–60 | MR | Zbl

[5] Ivashkovich S., Shevchishin V., “Structure of the moduli space in a neighborhood of a cusp-curve and meromorphic hulls”, Invent. Math., 136 (1999), 571–602 | DOI | MR | Zbl

[6] Kulikov Vik. S., Kharlamov V. M., “O breid-monodromnykh razlozheniyakh na mnozhiteli”, Izv. RAN. Ser. matem., 67:3 (2003), 79–118 | MR | Zbl

[7] Kulikov Vik. S., Taikher M., “Breid-monodromnye razlozheniya na mnozhiteli i diffeomorfnye tipy”, Izv. RAN. Ser. matem., 64:2 (2000), 311–341 | MR | Zbl

[8] Lalonde F., McDuff D., “The classification of ruled symplectic manifolds”, Math. Res. Lett., 3 (1996), 769–778 | MR | Zbl

[9] Li T.-J., Liu A.-K., “Symplectic structure on ruled surfaces and a generalized adjunction formula”, Math. Res. Lett., 2 (1995), 453–471 | MR | Zbl

[10] Micallef M., White B., “The structure of branch points in minimal surfaces and in pseudoholomorphic curves”, Ann. Math., 139 (1994), 35–85 | MR

[11] Moishezon B., “The arithmetic of braids and a statement of Chisini”, Contemporary Math., 164 (1994), 151–175 | MR | Zbl

[12] Moishezon B., Teicher M., “Braid group technique in complex geometry. I: Line arrangements in $\mathbb{CP}^2$”, Contemporary Math., 78 (1988), 425–555 | MR | Zbl