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Asymptotic growth of the number of classes of real plane algebraic curves when the degree increases

S. Yu. Orevkov·V. M. Kharlamov
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Abstract

The nonsingular real plane algebraic curves of given degree $d$ are considered either up to isotopy or up to deformation. The asymptotic behavior of the number $I_d$ of isotopy classes and the number $D_d$ of deformation classes are studied. It is shown, in particular, that $log I_d\asypt d^2$. Other related problems and their higher dimensional generalisations are discussed.

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S. Yu. Orevkov, V. M. Kharlamov. 2000-04-22. Asymptotic growth of the number of classes of real plane algebraic curves when the degree increases. https://arxiv.org/abs/math/0002213

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