2 problems

Let $C$ be an $M$-curve of even degree $m=2k$, with $p$ even ovals and $n$ odd ovals, and let $\chi=p-n$ be the Euler characteristic of the Ragsdale membrane. Ragsdale's $M$-curve…

Fix an integer $m\ge 1$, and consider real schemes of degree $m$, ordered in the lattice of all real schemes. A scheme is of type I when its real curve is dividing. Rohlin's maxima…