2 problems

Let $X$ be a symplectic $4$-manifold, let $f$ be a sufficiently high-degree pencil on $X$, and let $\mathcal{I}_f$ denote the integer-valued invariants counting sections of the ass…

Let $(X,\omega)$ be a simply connected symplectic $4$-manifold. For sufficiently large $k$, let $G_k^0$ be the relevant subgroup associated with the branch curve of the degree-…