6 problems

Let $X$ be an irreducible holomorphic symplectic $4$-fold, let $E$ be a nef line bundle on $X$, and let $L^*$ denote the map in the sheaf Lefschetz action. The sheaf Lefschetz inje…

Let $k$ be an algebraically closed field and let $i\colon X=V(f)\hookrightarrow\mathbb{P}^n_k$ be a closed embedding of a smooth irreducible hypersurface of degree $d$. For a bound…

Banach cohomology and comparison conjecture. There is an isomorphism of topological $K$-vector spaces

Let $\mathcal{A}$ be a hyperplane arrangement in a vector space of dimension $\ell$, let $L_0$ be its intersection lattice with the minimal element removed, and let $\mathscr{D}$ d…

Let $X \subseteq \operatorname{iGr}(n,2n)$ be the big affine cell, or a ball or a polydisc inside it, and let $Z$ be the corresponding twistor space in the stated double fibration.…

The singular BGG complex is constructed on the twistor space $Z'$ associated with a suitably chosen, but arbitrarily small, open subset $X'$. Local exactness conjecture. The conclu…