4 problems

Holomorphic section conjecture. There exists a holomorphic section of $M$ in all these examples.

Let $N$ be the degree of a positive line bundle over a Kähler manifold, and let $\mathcal{N}^{\operatorname{crit}}_{N,h}$ denote the expected number of critical points of random ho…

Let $m$ be the complex dimension of ${\mathbb C}{\mathbb P}^m$, and let $\mathcal{N}^{\operatorname{crit}}_{N,h}({\mathbb C}{\mathbb P}^m)$ denote the expected number of critical p…

Holomorphic-section conjecture. The disc bundle $L$ admits a holomorphic section if and only if