There is a need for (at least) two more dashed arrows in amssymbols : how to produce them?

Question

In birational geometry, we often use dashed arrows to insist on the fact that our maps are not defined everywhere. I wonder how can we produce:

1. a mapsto dashed arrow joining \mapsto and \dashrightarrow;
2. a circle dashed arrow like \circlearrowleft?

Answer 1

The first one is easy

 \def\dashmapsto{\mapstochar\dashrightarrow}

The second one if you mean the dashes go round the circle really needs a font with that character, that I don't know.

If you can't find a font, then there is always a gross hack available, you may want to tweak the rule widths a bit but...

\documentclass{article}
\usepackage{amssymb,color}

   \def\dashmapsto{\mathrel{\mapstochar\dashrightarrow}}
   \def\dashcirclearrowleft{\mathrel{\circlearrowleft\llap{{\color{white}%
\vrule height 0.2em width 0.3em depth 0em
\vrule width 0.2em  height 0.7em depth -.3em
\vrule width 0.3em  height 0em depth .2em
\vrule height 0.3em width 0.4em depth -.1em
}}}}

\begin{document}

\[a \mapsto  b \]
\[a \dashmapsto  b \]
\[a \circlearrowleft b\]
\[a \dashcirclearrowleft b\]

\end{document}