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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58758The 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.11 pages; a misprint in the table is correctedAlgebraic GeometryCombinatorics14P25;05A16Asymptotic growth of the number of classes of real plane algebraic curves when the degree increasestext