Asymptotic growth of the number of classes of real plane algebraic curves when the degree increases
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 Id of isotopy classes and the number Dd of deformation classes are studied. It is shown, in particular, that log Id d2. Other related problems and their higher dimensional generalisations are discussed.
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