12 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 $\alpha$ be a tautological class in the cohomology ring $H^\ast(\mathcal{M}_{g,n})$, let $\gamma_i\in H^\ast(\mathbb{C} A,\mathbb{R})$ be arbitrary insertions, and let…

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 $X$ be a variety of $K3^{[n]}$ type, let $beta e 0$ be an effective class in $H2(X,mathbb{Z})$, and define … where…

Let $S$ be a K3 surface, let $\beta$ be an effective curve class, and let the multiple-cover contributions be subtracted from its Gromov–Witten invariants. K3 surface divisibility-…

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…

Donaldson–Thomas multiple-cover formula. Assume $n>0$ or at least two of $d_1,d_2,d_3$ are positive. Then

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

Multiple-cover formula. For all $d_1,d_2>0$,

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…