Geodesic
The growth rate of the number of classes of real plane algebraic curves with the growth of the degree
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 218-233

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The work presents some results on the asymptotics of the number of real plane algebraic curves as the degree grows. In particular, we obtain the asymptotics of the number of curves considered up to the isotopy and rigid isotopy, as well as the number of isotopic classes of maximal curves realizable by $T$-curves. Some results are generalized onto hypersurfaces in non-singular algebraic varieties of arbitrary dimension. 
@article{ZNSL_2000_266_a12,
     author = {S. Yu. Orevkov and V. M. Kharlamov},
     title = {The growth rate of the number of classes of real plane algebraic curves with the growth of the degree},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {218--233},
     publisher = {mathdoc},
     volume = {266},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a12/}
}
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S. Yu. Orevkov; V. M. Kharlamov. The growth rate of the number of classes of real plane algebraic curves with the growth of the degree. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 218-233. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a12/