S. Orevkov

collaborators

2 papers

math.GT2003

Plane real algerbaic curves of odd degree with a deep nest

Stepan Yu Orevkov

We apply Murasugi-Tristram inequality to real algebraic curves of odd degree on $R P^{2}$ with a deep nest, i.e. a nest of the depth $k - 1$ where $2 k + 1$ is the degree. For such curves,…

math.AG2003

The number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves

V. Kharlamov, S. Orevkov

The number of topologically different plane real algebraic curves of a given degree $d$ has the form $exp (C d^{2} + o (d^{2}))$ . We determine the best available upper bound for the con…