14 problems

Let $X_v$ be a Schubert variety and let $e_u$ be a torus-fixed point. Write $\mathcal{I}_{\mathrm{not\ Gorenstein}}$ for the order ideal of intervals describing pairs $(u,v)$ for w…

Let $X_w$ be a Schubert variety, and let $X_v$ range over the Schubert varieties contained in its maximal singular locus. The maximal non-Gorenstein locus characterization proposes…

Let $(X,o)$ be a Gorenstein surface singularity with integral homology sphere link, and let its splice diagram encode the topology of the link. Gorenstein splice-type conjecture.…

A Gorenstein singularity is a singularity associated with the higher-dimensional orbifold and resolution framework described in the source. Higher-dimensional CFT conjecture. A con…

A Gorenstein singularity is a singularity of the type considered in the source, with associated discrete-group and cohomological data. Higher-dimensional CFT conjecture. There exis…

Let $X$ be a variety with mild Gorenstein singularities, and let $\widehat X_1$ and $\widehat X_2$ be smooth crepant resolutions of $X$, when such resolutions exist. Resolution-ind…

Let $X$ be an algebraic variety with Gorenstein singularities. Write $H^*_{\rm st}(X)$ for a prospective cohomology theory associated with $X$. String-theoretic cohomology conjectu…

Let $Q\subset\mathbb{R}^k$ be a lattice polytope with associated Gorenstein cone … Suppose $Q$ is lattice equivalent to a face $F$ of a lattice polytope $P\subset\mathbb{R}^n$. Let…

Let $(R,\mathfrak m)$ be a $d$-dimensional Gorenstein local domain essentially of finite type over $\mathbb{C}$. Gorenstein positivity conjecture. If $\operatorname{Spec} R$ has kl…

Let $X=X_P$ be the affine toric Gorenstein variety associated with the polytope $P$, and let $T^1_X$ denote its first-order deformation space. Suppose the deformations of $X$ are c…

Let $(C,\eta)$ be a generalised multiscale differential with tropicalisation $\lambda$. For every level $i$, let $\lambda_i$ denote the truncation of $\lambda$ to that level, and l…

The multiplicities $m_i-2$ are determined by the singularity $(C,p)$ via its conductor, and hence determine a stratum of holomorphic differentials. Connected-component conjecture.…

For each integer $n\geq 1$, let $s_n$ be the sequence used in the paper, let $h=s_n-1$, and let $X$ be the $n$-fold weighted projective space in the theorem with weights…

Let $X$ be a Schubert variety, and let $x\in X$. The Gorenstein-locus conjecture. The point $x$ lies in the Gorenstein locus of $X$ if and only if the generic point of every irredu…