4 problems

Mukai's conjecture. One has

Let $X$ be a Fano manifold of Picard number $1$, and let $f:X\to X$ be a surjective endomorphism. Here, $\deg f$ denotes the degree of $f$, and $\mathbb{P}^n$ denotes projective…

Sato's conjecture. $X$ is a projective space.

Bonavero–Casagrande–Debarre–Druel conjecture. One has