7 problems

Let $C$ be a smooth real plane curve, and call an oval empty when its interior contains no other real component. Itenberg–Viro contraction conjecture. Any empty oval of $C$ can be…

Degtyarev's conjecture. If $g(\SS)>0$, then $\SS$ is realized by exactly two rigid isotopy classes of irreducible sextics, one abundant and one not. If $g(\SS)=0$, then $\SS$ is re…

Let $A_0$ and $A_1$ be real pseudoholomorphic curves in $\mathbb{CP}^2$, with each $A_k$ holomorphic for a tame complex-conjugation-invariant almost complex structure. Two such cur…

Let $K$ be a smooth, irreducible real algebraic curve in $\mathbb P^3$ of degree $d\geq 3$, let $N_d=(d-1)(d-2)/2$, and suppose $K$ is an $MW$-curve with $w(K)=N_d$. The projective…

Let a smooth real plane curve be of even degree, so that an oval is null-homotopic in $\mathbb RP^2$. Call a scheme rigid when any two curves representing it are rigid-isotopic. On…

Let $C_m$ be any smooth real plane curve of degree $m$, and let its empty ovals be the components whose interiors contain no other real components. Collective contraction conjectur…

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…