11 problems

Let $k$ be a field and let … be a reduced monomial hypersurface. For a nonnegative integer $m$, let $\mathcal{W}_{m}(X)$ denote its truncated wedge scheme. An irreducible component…

Jet-point counting conjecture. Then there exists a constant $D$ such that

Let $k$ be an algebraically closed field of characteristic $0$, let $f\in k[[x_{1},...,x_{n}]]$ define an isolated singularity at $0$, and let $J(f)$ be the Jacobian ideal of $f$.…

Let $k$ be an algebraically closed field of characteristic $0$, let $R=k[[x_{1},...,x_{n}]]$ with maximal ideal $\mathbf{m}$, and let $f\in R$ be a weighted homogeneous polynomial.…

Shellability and Hilbert-series conjecture. The abstract simplicial complex corresponding to $\tilde{I^{m,n}_{r,k}}$ is shellable, and the Hilbert series of the principal component…

Let $n\in\mathbb N$, let $I\subset(x_1,\dots,x_{n+c})$ define the $n$-dimensional variety $X=\operatorname{Spec}k[x_1,\dots,x_{n+c}]/I$, and let $s_m(0;X)$ be the jet-scheme invari…

The semicontinuity conjecture for minimal log discrepancies. The function

Let $r$ and $k$ be positive integers, and let $I^{2r+1,k}_r$ denote the jet pfaffian ideal associated with the ideal of size-$2r$ pfaffians of a generic $(2r+1)\times(2r+1)$ skew-s…

Let $X$ be a $d$-dimensional variety, let $x\in X$ be a closed point, and let $s_m(X,x)=(m+1)d-\dim X_m(x)$, where $X_m(x)$ is the local $m$-jet scheme at $x$. Let $\delta$ be an i…

Let $X$ be a variety of dimension $d$, let $x$ be a closed point of $X$, and define … where $X_m(x)$ is the local $m$-jet scheme of $X$ at $x$. Finite determination conjecture. For…

Finite jet detection conjecture. There is a number $N_{\delta,d}$ depending only on $\delta$ and $d$ such that, if