8 problems

Let $M$ be a compact complex manifold. An algebraic foliation is a foliation on a projective variety defined in the algebraic category, and a submanifold is transverse to the folia…

Let $R\subset\mathbb{C}$ be a finitely-generated $\mathbb{Z}$-algebra, and let $M$ be a smooth $R$-scheme. A foliation $\mathscr{F}\subset T_{M/R}$ is a sub-bundle of Lie algebras.…

Let $X$ be a normal complex quasi-projective variety, and let $\mathcal{F}\subset T_X$ be a coherent subsheaf closed under the Lie bracket. The distribution $\mathcal{F}$ is algebr…

Let $(X,\mathcal{F},B,\mathbf{M})$ be a generalized foliated quadruple. Here ACSS denotes the technical condition defined in the source, and F-dlt denotes foliated divisorial log t…

Let $(X,\mathcal{F},B)$ be a $\mathbb{Q}$-factorial projective foliated triple, such that $\mathcal{F}$ is algebraically integrable, $B$ is a $\mathbb{Q}$-divisor, $(X,B)$ is klt,…

Let $X$ be a compact Kähler manifold whose canonical bundle $K_X$ is pseudo-effective, and let $\mathcal{F}\subset T_X$ be a holomorphic foliation with $c_1(\mathcal{F})=0$. A foli…

Finiteness conjecture. If $D$ is simple, then

Quasi-line foliation conjecture. There exists a birational map