May I recommend to use the more modern package tikz-cd? This would look like this:
% arara: pdflatex
\documentclass{article}
\usepackage{tikz-cd}
\usepackage{mathtools}
\DeclareMathOperator\spec{spec}
\begin{document}
\[
\begin{tikzcd}[every arrow/.append style={hook}]
& \spec K & \\
\spec K(x)\arrow{ur} & & \spec K(y)\arrow{ul} \\
& \spec k(s)\arrow{ur}\arrow{ul} &
\end{tikzcd}
\]
\end{document}
If you want to stick to dcpic
, you may use the starred version of \DeclareMathOperator
as a workaround.
% arara: pdflatex
\documentclass{article}
\usepackage{pictexwd,dcpic}
\usepackage{mathtools}
\DeclareMathOperator*\spec{spec} % Asterisk added
\begin{document}
\begindc{\commdiag}[500]
\obj(0,0){$\spec k(s)$}
\obj(0,2){$\spec K$}
\obj(-1,1){$\spec k(x)$}
\obj(1,1){$\spec k(y)$}
\mor(0,0)(-1,1){}[+1,6]
\mor(0,0)(1,1){}[-1,6]
\mor(-1,1)(0,2){}[+1,6]
\mor(1,1)(0,2){}[+1,6]
\enddc
\end{document}