7 problems

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.…

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 $Q\subset\mathbb{R}^k$ 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 $(C,\eta)$ 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…

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…