I imagine the answer is no. But is there a connection between the following two definitions of a fat point (at least morally, since not mathematically):
1) (Say for a $k$-scheme $X$) a map $\text{Spec}(k[x]/(x^n))\to X$ for $n>1$ (or whatever is appropriate more generally, but we're mapping from a point scheme with a non-reduced structure)
2) (Let $S$ be a noetherian scheme) A fat point laying over a $k$-point $x:\text{Spec}(k)\to S$, is a triple $(x_0,x_1,R)$ where $R$ is a DVR, $x_0:\text{Spec}(k)\to \text{Spec}(R)$, and $x_1:\text{Spec}(R)\to S$ are such that 1) $x=x_1\circ x_0$, 2) Th…
1) (Say for a $k$-scheme $X$) a map $\text{Spec}(k[x]/(x^n))\to X$ for $n>1$ (or whatever is appropriate more generally, but we're mapping from a point scheme with a non-reduced structure)
2) (Let $S$ be a noetherian scheme) A fat point laying over a $k$-point $x:\text{Spec}(k)\to S$, is a triple $(x_0,x_1,R)$ where $R$ is a DVR, $x_0:\text{Spec}(k)\to \text{Spec}(R)$, and $x_1:\text{Spec}(R)\to S$ are such that 1) $x=x_1\circ x_0$, 2) Th…