4 problems

Let $\mathcal{F}$ be a regular foliation of rank $p$ on a smooth projective variety $X$, and let $L$ be an ample line bundle on $X$. Foliated Fujita conjectures. The line bundle ……

Let $(M,\mathcal F)$ be a codimension-one foliation of a closed manifold that is transversely $C^2$, with exceptional minimal set $\Lambda$. A semi-exceptional leaf is a boundary l…

Let $(M,\mathcal F)$ be a codimension-one foliation of a closed manifold that is transversely $C^2$, with exceptional minimal set $\Lambda$. Dippolito's conjecture. There exists a…

Anosov's conjecture. A generic polynomial foliation has no identical cycles.