Geodesic
Rigid isotopies of real trigonal curves on the Hirzebruch surfaces
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 133-142

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A rigid isotopy of nonsingular real algebraic curves on a scroll is a path in the space of such curves of a given bidegree. For real algebraic curves of bidegree $(m,3)$ on the Hirzebruch surface $\Sigma_1$ (the projective plane with a point blown up) we obtain the rigid isotopy classification of nonsingular curves and give some corollaries for the space of curves with a single node or a cusp on a hyperboloid and on $\Sigma_2$. 
@article{ZNSL_2000_267_a6,
     author = {V. I. Zvonilov},
     title = {Rigid isotopies of real trigonal curves on the {Hirzebruch} surfaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {133--142},
     publisher = {mathdoc},
     volume = {267},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a6/}
}
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V. I. Zvonilov. Rigid isotopies of real trigonal curves on the Hirzebruch surfaces. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 133-142. http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a6/