3 problems

Let $(X,\omega)$ be a compact symplectic manifold, let $\mathcal D=\bigcup_{i=1}^m\mathcal D_i$ be a normal crossing divisor, and let $L\subset X\setminus\mathcal D$ be a compact r…

Let $X$ be a smooth projective variety and let $D=D_1+\cdots+D_n$ be an effective reduced normal crossing divisor with each $D_i$ smooth, irreducible, and nef. Let $I_1,\ldots,I_m$…

Let $X$ be a smooth projective variety and let $D=D_1+\cdots+D_n$ be an effective reduced normal crossing divisor whose components $D_i$ are smooth, irreducible, and nef. For a cur…