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

Publication date: 25 February 2000

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

l o g I_{d} a s y p t d^{2}

. Other related problems and their higher dimensional generalisations are discussed.

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