5 problems

Let $X$ be a toric Calabi–Yau 4-fold and let $\curly P=\curly P_v^{(q)}(X)$ for $q\in\{-1,0,1\}$. Toric fixed-locus conjecture. If $\curly P^{T_X}$ is zero-dimensional, then…

Let $X$ be a Calabi–Yau 4-fold with an algebraic torus $T$ acting while preserving the Calabi–Yau volume form, and let $L$ be a $T$-equivariant line bundle on $X$. For…

Let $X$ be a quasi-projective Calabi–Yau 4-fold, and let $\curly P=\curly P_v^{(q)}(X)$ be the relevant PT$_q$ moduli space. Assume that $\curly P$ is projective, so that its virtu…

Fix plane partitions $\boldsymbol{\mu}=\{\mu_a\}_{a=1}^{4}$ corresponding to $(\mathbb C^*)^3$-fixed subschemes of $\mathbb C^3$ of dimension at most one, viewed as asymptotic cros…

Let $X$ be a projective Calabi-Yau 4-fold and $L$ a line bundle on $X$. For any $gamma in H^4(X,mathbb Q)$ and $beta in H^6(X,mathbb Q)$, choose orientations of the relevant moduli…