5 problems

Conjecture on the two flopped Kähler cones. These two neighbouring regions are the Kähler cones of $X'^{(1)}$ and $X”^{(1)}$.

Conjecture on the flopped Kähler cone. The cone on the other side of the boundary separating it from $\mathcal{K}(X)$ is the Kähler cone of $X'$.

Conjecture on the flopped nef cone. The cone adjacent to $\mathcal{K}(X)$ across the shared vertical boundary, shown as the green region, is the nef cone of $X'$.

Let $X$ be a complex surface and let $L$ be a line bundle on $X$. Its cohomology dimensions are the dimensions of the groups $H^i(X,L)$ as functions of the line-bundle data. Piecew…

Let $X$ be a manifold of complex dimension $n$, and let $L$ be a line bundle on $X$. Its cohomology dimensions are the dimensions of the groups $H^i(X,L)$ as functions of the data…