• Reading about symmetric product, by Dykerhoff-Jasso-Lekili and Auroux's ICM.
• Idea about generation

How to understand it? Downstairs, we have $Sym^2(\C^*)$, which we can shrink to $Sym^2(S^1)$. Upstairs, I just don't know what to put over the diagonal. We know the fiber of the diagonal is $\C^* \times \C_u$, and the superpotential is basically the variable $u$, so if we just ask for the fiberwise skeleton, it is zero.

Same thing, if we ask for the multiplicative case. The fiberwise skeleton of a smooth fiber is $(S^1)^2$, then become subcritical for the special fiber.