7 problems

Let $(Y,D)$ and $(Y',D')$ be $n$-dimensional, deformation-equivalent log Calabi–Yau pairs, where a log Calabi–Yau pair is a smooth projective variety together with an anticanonical…

Let $X_1$ and $X_2$ be Fano varieties with mirror Landau–Ginzburg models $(X_1^\vee,W_1)$ and $(X_2^\vee,W_2)$. Write $\pi_{W_i}(t)$ for the classical period of the model, and let…

Rigidity converse. Suppose that for every strong generalized cycle decomposition $X_1, \dots, X_n$, the induced reordering $\tau$ is the identity, except that if some series class…

Local Torelli conjecture. The following hold: (a) away from points of $C'$, the fibers of $\alpha$ are smooth or empty; and (b) for a smooth point $p'$ of $C'$, the corresponding p…

For a smooth curve $C$, let $W^r_d(C)$ denote the Brill–Noether locus of line bundles of degree $d$ with at least $r+1$ sections, and let $\operatorname{OC}_3(W^0_d(C),L)$ be the o…

Right-equivalence Torelli conjecture. The map $LBL$ is injective.

Canonical Brieskorn-lattice Torelli conjecture. The map $BL$ is injective.