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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2000 Volume 266, Pages 218–233 (Mi znsl1254)

This article is cited in 6 papers

The growth rate of the number of classes of real plane algebraic curves with the growth of the degree

S. Yu. Orevkovab, V. M. Kharlamovc

a Steklov Mathematical Institute, Russian Academy of Sciences
b Université Paul Sabatier
c University Louis Pasteur

Abstract: The work presents some results on the asymptotics of the number of real plane algebraic curves as the degree grows. In particular, we obtain the asymptotics of the number of curves considered up to the isotopy and rigid isotopy, as well as the number of isotopic classes of maximal curves realizable by $T$-curves. Some results are generalized onto hypersurfaces in non-singular algebraic varieties of arbitrary dimension.

UDC: 512.77

Received: 10.10.1999


 English version:
Journal of Mathematical Sciences (New York), 2003, 113:5, 666–674

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