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

2000/02/25 by S. Yu. Orevkov, Orevkov, S. Yu., V. M. Kharlamov +1
Mathematics · #05A16 #14P25 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:05A16 #msc:14P25

paper · pdf · doi:10.48550/arxiv.math/0002213

11 pages; a misprint in the table is corrected

arxiv created 2000/04/22 · arxiv updated 2009/11/30

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 log I_d\asypt d². Other related problems and their higher dimensional generalisations are discussed.

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