7 problems

Let $S$ be a K3 surface, let $\beta\in H_2(S,\mathbb{Z})$ be an effective curve class, and let $\langle \tau_{k_1}(\gamma_1) \cdots \tau_{k_n}(\gamma_n) \rangle^S_{g,\beta}$ denote…

Let $A$ be an abelian surface, let $\beta\in H_2(A,\mathbb{Z})$ be effective, and for each divisor $k\mid\beta$ choose an abelian surface $A_k$ and a parallel-transport morphism…

Let $X$ be a variety of $K3^{[n]}$ type and let $\beta\in H_2(X,\mathbb{Z})$ be effective. For each divisor $k\mid\beta$, choose a variety $X_k$ of $K3^{[n]}$ type and a parallel t…

Let $S$ be a K3 surface, let $\alpha$ be a charge, and let $\chi_S(\alpha,\alpha)$ denote its Mukai pairing. Write $[r]_t=(t^{r/2}-t^{-r/2})/(t^{1/2}-t^{-1/2})$, and let…

Multiple-cover formula. For all $g\geq2$, $d_1,d_2>0$, and $d_3\geq0$,

Let $S$ be a K3 surface, let $\Gamma_0$ be the lattice of Mukai classes used for the sheaf-counting invariants, and let $(v,v)$ denote the Mukai pairing. For $k\mid v$, assume…

Let $S$ be a K3 surface, let $\widetilde{H}(S,\mathbb{Z})=\mathbb{Z}\oplus H^2(S,\mathbb{Z})\oplus\mathbb{Z}$ be its Mukai lattice, and let $v$ be an algebraic class in this lattic…