6 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…

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 $C$ be the local curve considered in the paper, let $N_{n,\gamma}$ denote the corresponding generalized DT invariant for $(n,\gamma)\in\mathbb{Z}\oplus H_2(C,\mathbb{Z})$, and…

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