4 problems

Anti-diagonal equivariant GW correspondence. The identity

Let $X=\operatorname{Tot}_{\mathbb P^1}(\mathcal O(-1)\oplus\mathcal O(-1)\oplus\mathcal O)$, and let $\mathcal Z_X(y,q,Q)=\sum_{n,d}P_{n,d[\mathbb P^1]}(\mathcal O,y)q^nQ^d$ be it…

Let $X_1$ be the resolved conifold $\mathcal{O}_{\mathbb{P}^1}(-1)\oplus\mathcal{O}_{\mathbb{P}^1}(-1)$ equipped with the anti-diagonal action, and consider its equivariantly Calab…

Let $\Psi^{(a)}_{0,1}(t;x)$ be the resolved-conifold open-string one-point function, and set $Q=-e^{-t}$. Half-integrality conjecture. There are half-integers $e^{(a)}_{k,m}$ such…