68 problems

Let $\Delta$ be a convex lattice polygon containing the origin in its interior. A Laurent polynomial $W$ has Newton polygon $\Delta$, and a pair $(G,D)$ consists of a consistent di…

Let $M \to B$ and $\check{M} \to B$ be dual torus fibrations arising in the SYZ picture, and let a Lagrangian section of $M \to B$ be a Lagrangian submanifold mapping isomorphicall…

Fix a field $k$ and positive integers $p_0,\ldots,p_n>1$. For each $i$, let $W_{p_i}(X_i)\in\mathbb{C}[X_i]$ be a general polynomial of degree $p_i$, and set … Let…

Let ${\cal C}^A$ be the cyclic $A_\infty$-category obtained from Fukaya's $A_\infty$-category $(V^F,\eta^F,{\frak m}^F)$ by suspension, and let ${\cal C}^B$ be the cyclic…

Let $X$ and $Y$ be mirror varieties, let $\mathcal{F}uk(X)$ denote the Fukaya category of $X$, and let $D^b\operatorname{Coh}(Y)$ denote the bounded derived category of coherent sh…

Let $\check X$ be a toric variety with $d$ rays in its fan, and let $T$ be an algebraic torus of rank $\dim(\check X)$. Let $V(E_A)$ be the hypersurface cut out by the principal…

Let $X_{\mathrm{res}}$ be the resolution of the $A_n$ surface singularity, let $D_r$ be the indicated divisor, and let $\sigma$ be a stop. Let $s$ be a formal parameter, with coeff…

Let $X_{\mathrm{res}}$ be the resolution of the $A_n$ surface singularity, let $D_r$ be the indicated divisor, and let $s$ be a formal parameter with coefficient field…

Let $(Z,\check{Z})$ be a Batyrev--Borisov mirror pair, with $Z$ and $\check{Z}$ smooth subvarieties of Fano toric varieties $X_{\Sigma}$ and $X_{\check{\Sigma}}$ associated to dual…

Let $\Xfr$ be a smooth semiprojective toric variety. The category $\Sh_{\Lambda_\mathrm{Cox}}(M_\RR / M)$ is closed under $\otimes_k$. Cox category tensor-product conjecture. There…

Let $(X,D)$ be a log Calabi–Yau manifold, with $D$ an anticanonical divisor of $X$, and let $W_X\colon \check X\to\mathbb C$ be a mirror of $(X,D)$. Let $\widehat{\Lambda}_{\geq}$…

Let $X_\Sigma$ be the toric variety with Givental–Hori–Vafa mirror $W_\Sigma$, and let $\widehat{\Lambda}_{\geq}$ denote the Novikov ring. Write…

Let $W$ be an invertible weighted homogeneous polynomial in $n+1$ variables, let $\check{W}$ be its Berglund–Hübsch transpose polynomial, and let $\Gamma_W$ be the group acting dia…

Berglund–Hübsch homological mirror symmetry conjecture. There exists a derived equivalence between $\mathcal{F}(W,G)$ and $\mathcal{MF}(W^T,G^T)$.

Let $\bfW$ be an invertible polynomial not of Calabi--Yau type, let $U$ be the associated quotient stack, let $\Uv$ be the corresponding Milnor fiber, and let $\scoh U$ and…

Let $X_b$ be a fiber of a Calabi–Yau threefold family and let $\hat X_0$ be its mirror. Write $F_B^\bullet$ and $F_A^\bullet$ for the Hodge filtrations on the respective stalks, le…

Auroux's mirror correspondence conjecture. Under homological mirror symmetry, $\rho$ corresponds to the composite of $q$ with the Knörrer periodicity equivalence; $\alpha_0$ corres…

Let $Q_{d53f\mathbb{R}P^2}$ denote the matrix factorization corresponding, under homological mirror symmetry, to the monotone Lagrangian $(\mathbb{R}P^2,b=0)$, and let … Here…

Let $\overline{\mathcal{Y}}_{n,k}$ and $\overline{\mathcal{Z}}_{n,k}$ be the compactifications of $\mathcal{Y}_{n,k}$ and $\mathcal{Z}_{n,k}$ described in the source, let…

Let $V_{n,k}$ be the symmetric-square-type Liouville space considered in the paper, equipped with its natural integer grading $\eta_0$, and let $\mathcal{Z}_{n,k}$ be the special f…

Let $A=(a_{ij})$ be an $(n+1)\times(n+1)$ integer matrix with nonzero determinant, and define … Let $\check{{\bf w}}$ be the polynomial associated to $A^T$, let $\Gamma_{\bf w}$ be…

Let $\mathbf{w}$ be an invertible polynomial with admissible symmetry group $\Gamma\subseteq\Gamma_{\mathbf{w}}$, and let $\widecheck{\Gamma}$ be the corresponding dual group. Let…

Let $\mathbf{w}$ be an invertible polynomial with admissible symmetry group $\Gamma\subseteq\Gamma_{\mathbf{w}}$, and let…

Let $X$ be the noncompact toric variety considered in the paper, with K-groups $K(X)$ and $K^c(X)$ paired by … Choose bases $\{F_1,\ldots,F_d\}$ of $K(X)$ and $\{S_1,\ldots,S_d\}$…

Let $X$ be a noncompact toric Calabi–Yau variety and let $Y$ be its Hori–Vafa mirror. For mirror objects … write $Z_t(E)$ for the central charge of $E$ and $C_t(L)$ for the central…