Counterexamples to a conjecture of Rokhlin (Q1072611)

By a scheme of degree m is meant a scheme of relative position of ovals in the projective plane of a real curve of degree m. A scheme of degree m is of type I if any curve of degree m with the given scheme divides its complexification and is of type II if all curves of degree m with the given scheme do not divide their complexifications. A scheme is called maximal if it is not part of a larger scheme of the same degree. \textit{V. A. Rokhlin} [Usp. Mat. Nauk 33, No.5(203), 77-89 (1978; Zbl 0437.14013)] made the conjecture that a maximal scheme is of type I. This assertion is valid for schemes of degree \(\leq 7\). In the paper under review the author proves that there exists a maximal scheme of degree 8, which is of type II. So the Rokhlin conjecture is disproved.