10 problems

Full strange duality conjecture. The morphism $SD$ is an isomorphism. This is the global formulation of the full strange-duality statement for the generalized Verlinde bundles; the…

Strange duality conjecture. For any $g\geq6$, this map is an isomorphism.

Verlinde–Segre correspondence. The universal series satisfy

Assume a general sheaf in $M(e)$ is locally free, let $V$ have Chern character $e^*+f$, and assume $\chi(e\cdot f)=0$. Let $\operatorname{Quot}(V,f)$ parametrize quotients…

Universal-series correspondence. The series satisfy

Let $X$ be a simply connected elliptic surface with a section and at worst nodal fibers, and let $v$ and $w$ be orthogonal topological types of ranks $r,s\geq 2$ satisfying … and ……

Mukai strange-duality conjecture. The duality morphism $\mathsf {D}$ is either an isomorphism or zero. Numerical symmetry and vanishing results motivate this dichotomy, while the p…

Beauville's symplectic strange-duality conjecture. The morphism $\mathsf {D}$ is an isomorphism. Beauville established equality of the dimensions of the two spaces of sections, but…

Let $v$ be a Mukai vector, and let $F_{1}$ and $F_{2}$ be sheaves with the same Mukai vector orthogonal to $v$. Let $\Theta_{F_i}$ denote the corresponding theta line bundles on th…

Let $A$ be the abelian surface and let $v$ and $w$ be Mukai vectors satisfying Assumptions and, with the associated moduli spaces and determinant line bundles as in the paper. Deno…