7 problems

Let $X_k=\mathcal O(k)\oplus\mathcal O(-2-k)\rightarrow\mathbb{P}^1$ carry the diagonal torus action $\lambda_1=\lambda_2$, and let…

Let $X_k=\mathcal O(k)\oplus\mathcal O(-2-k)\rightarrow\mathbb{P}^1$ carry the antidiagonal torus action $(\lambda,-\lambda)$ on the bundle, and let $t_k$ denote the Kähler class o…

Rationality, symmetry and pole-structure conjecture. For any $X$ and $T$ as above: (1) every $\mathbf z$-coefficient of the disconnected and connected descendent invariants is the…

Let $X=\mathcal O_{\mathbb P^1}(-1,-1,0)$ and let $T$ be the Calabi–Yau torus, with equivariant parameter $\lambda_3$. Let $P^{\mathrm{JS}}_{n,d}$ denote the $T$-equivariant Joyce–…

Let $X=\mathcal{O}_{\mathbb{P}^{1}}(l_1,l_2,l_3)$ with $l_1+l_2+l_3=-2$, and let $\mathrm{GW}_{0,2}(X)$ and $P_{1,d[\mathbb{P}^{1}]}(X)$ denote the equivariant invariants defined i…

Let $Y=\operatorname{Tot}_{\mathbb P^1}(\mathcal O_{\mathbb P^1}(l_1)\oplus\mathcal O_{\mathbb P^1}(l_2))$ with $l_1+l_2\geq -1$, and let $d$ be a positive degree. Denote by…

Denominator conjecture. The denominators of these partition functions are products of factors of the form $q^k$ and