4 problems

Beltrametti–Sommese conjecture on effective strictly nef divisors
arXiv@arxiv
Beltrametti–Sommese conjecture. If $D-K_X$ is nef, then $D$ is ample.
Conjectureopenalgebraic-geometry ample-divisors positivity
0
Existence conjecture for stable bundles on ample divisors of Calabi–Yau threefolds
arXiv@arxiv
Existence conjecture. There exists a stable vector bundle $V$ on $D$ such that
Conjectureopenample-divisors calabi-yau-threefolds stable-bundles
0
The rational-curve ampleness conjecture for nef divisors on hyperkähler manifolds
arXiv@arxiv
Rational-curve ampleness conjecture. $D$ is ample.
Conjectureopenample-divisors hyperkahler-geometry rational-curves
1
The extension conjecture for projective-bundle divisors
arXiv@arxiv
Extension conjecture. Then $d\ge b-1$ , and $(X,L)\cong (\mathbb{P}(\mathcal{E}),\xi_{\mathbb{P}})$ for an ample vector bundle $\mathcal{E}$ on $Z$ , with $p$ equal to the restrictio…
Conjectureopenalgebraic-geometry ample-divisors projective-bundles
0