An extremal property of Rokhlin's inequality for real algebraic curves (Q1910177)

An island of a nonsingular real algebraic curve of even degree is an outermost oval of the real algebraic curve, together with all ovals contained in it. An island is even if it consists of an even number of ovals. \textit{V. A. Rokhlin} derived inequalities for even degree nonsingular real algebraic curves and introduced the notion of complex orientations on such curves. An extremal property of Rokhlin's inequality is derived for those real algebraic curves in which every island is even. This extremal property disqualifies certain complex orientations on such real algebraic curves.