Geodesic
Real $J$-curves with deep nests on ruled surfaces
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 88-118

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The paper is divided in two independent parts. The goal of the first part (§ 2) is to present a new proof of the complex orientation formula obtained by S. Yu. Orevkov's [9], which allows one to generalize this formula to $J$-curves with deep nests on ruled surfaces. In particular, this yields an analog of this formula for separating real algebraic curves in $\mathbb C P^2$ with two nests. In the second part (§ 3), analogs of the inequalities of Arnol'd [1] and Rokhlin [11] are obtained for separating real $J$-curves with deep nests on ruled surfaces. 
@article{ZNSL_2000_267_a4,
     author = {J.-Y. Welschinger},
     title = {Real $J$-curves with deep nests on ruled surfaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--118},
     publisher = {mathdoc},
     volume = {267},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a4/}
}
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J.-Y. Welschinger. Real $J$-curves with deep nests on ruled surfaces. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 88-118. http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a4/