Geodesic
Topology of real algebraic curve complement in~$\mathbb CP^2$
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part IV, Tome 122 (1982), pp. 137-145

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The author studies homotopy tipe of $\mathbb CP^2\setminus(A\cup\mathbb RP^2)$ for real non-singular algebraic curve $A$ in $\mathbb CP^2$. In common case the results announced in the paper are partial one, but under some condition the homotopy tipe is determined completly. 
@article{ZNSL_1982_122_a13,
     author = {S. M. Finashin},
     title = {Topology of real algebraic curve complement in~$\mathbb CP^2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {137--145},
     publisher = {mathdoc},
     volume = {122},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_122_a13/}
}
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S. M. Finashin. Topology of real algebraic curve complement in~$\mathbb CP^2$. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part IV, Tome 122 (1982), pp. 137-145. http://geodesic.mathdoc.fr/item/ZNSL_1982_122_a13/