Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Hermite expressed a root of any degree 5 polynomial through elliptic integrals. It would be interesting if there are roots which cannot be expressed this way.
Don't know a reference, but (I think) if you have a sequence of Kahler classes converging to $\omega$ and destabilizing subsheaves $F_i$ for each, you can estimate $L^2$-integrals of the curvature of $F_i$, and this would imply that the sequence $F_i$ has a converging subsequence which converges to a subsheaf destabilizing $\omega$.
