Real J-Curves with Deep Nests on Ruled Surfaces

Research paper by J.-Y. Welschinger

Indexed on: 01 Mar '03Published on: 01 Mar '03Published in: Journal of Mathematical Sciences


A new proof of S. Yu. Orevkov's complex orientation formula is presented, which allows one to generalize this formula to J-curves with deep nests on ruled surfaces. In particular, an analog of this formula for separating real algebraic curves in \(\mathbb{C}P^2 \) with two nests is obtained. For separating real J-curves with deep nests on ruled surfaces, analogs of the Arnol'd and Rokhlin inequalities are obtained. Bibliography: 17 titles.