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

Stepan Orevkov (1) , Viatcheslav Kharlamov (2)

1 LEP - Laboratoire Émile Picard
2 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Matière Molle [cond-mat.soft]

Stepan Orevkov, Viatcheslav Kharlamov. Asymptotic growth of the number of classes of real plane algebraic curves when the degree increases. Journal of Mathematical Sciences, 2003, 113, pp.666-674. ⟨10.1023/A:1021158529011⟩. ⟨hal-00110818⟩