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

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

2000-02-25

arxiv.org/abs/math/0002213v2

Mathematics

Algebraic Geometry

11 pages; a misprint in the table is corrected

Scientific paper

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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