3 problems

Generic nondegeneracy conjecture. For generic $z$, all rational functions with prescribed ramification data $z$ and $\{\mathbf w\}$ are nondegenerate.

Transversality conjecture. For generic $z$, the intersection $\mathcal{I}_{\{\mathbf w\}}(z)$ is transversal and consists only of nondegenerate $p$-planes. In particular, for gener…

Identify $\mathbb{RP}^n$ with polynomials of degree at most $n$ up to a nonzero constant factor, and let $W_{k,n}:G_{k+1,n+1}\to\mathbb{RP}^{(k+1)(n-k)}$ be the Wronski map. Let…