4 problems

Let $\b X$ be a formal curve with associated numerical monoid … For a numerical monoid, let the associated numerical monoid of a blowup be the numerical monoid corresponding to its…

Let $R$ be a local complete Noetherian domain with coefficient field $k$, and set $X:=\operatorname{Spec}R$. For every $n\in\mathbb{N}_0$, consider the $n$-th Nash blowup…

Let $k$ be a field of characteristic zero, let $X$ be a variety of dimension $d$, and let $J\subseteq X$ be the Jacobian subscheme. Denote by $J^{(d-1)}$ its $(d-1)$-th neighborhoo…

Let $f$ and $g$ be germs in the convergent power series ring $\mathbb C\\{\mathbf{x}\\}$, with $f(\mathbf{0})=g(\mathbf{0})=0$. Two germs are contact equivalent at the origin if on…