“Broken” arrow symbol

The MnSymbol package provides it.

\documentclass{article}
\usepackage{MnSymbol}
\begin{document}
So a rational map f: $V_1 \dashedrightarrow V_2$ is not a map at all;
\end{document}

You can also use the usual overkill option of tikz which then gives you all the flexibility inherent in tikz. Here are a few of the possible options:

\documentclass{article}
\usepackage{tikz}

\newcommand*{\DashedArrow}[1][]{\mathbin{\tikz [baseline=-0.25ex,-latex, dashed,#1] \draw [#1] (0pt,0.5ex) -- (1.3em,0.5ex);}}%

\begin{document}
$V_1 \DashedArrow V_2$\par

\medskip
$V_1 \DashedArrow[densely dashed    ] V_2$\par
$V_1 \DashedArrow[dotted            ] V_2$\par
$V_1 \DashedArrow[densely dotted    ] V_2$\par
$V_1 \DashedArrow[densely dashdotted] V_2$\par

\medskip
$V_1 \DashedArrow[->,densely dashed    ] V_2$\par
$V_1 \DashedArrow[->,dotted            ] V_2$\par
$V_1 \DashedArrow[->,densely dotted    ] V_2$\par
$V_1 \DashedArrow[->,densely dashdotted] V_2$\par
\end{document}

While MnSymbol provides \dashedrightarrow, it actually provides a whole host of math symbols as an entire font, which might have an unwanted effect. As such, it is possible to create your own \dashedrightarrow:

\documentclass{article}
\usepackage{color}% http://ctan.org/pkg/color
\makeatletter
\newcommand{\dashedrightarrow}[1][2pt]{%
  \settowidth{\@tempdima}{$\rightarrow$}\rightarrow% typeset arrow
  \makebox[-\@tempdima]{\hskip-1.5ex\color{white}\rule[0.5ex]{#1}{1pt}}% typeset overlay
  \phantom{\rightarrow}% advance appropriate horizontal distance
}
\makeatother
\begin{document}
\begin{tabular}{lc}
  \verb|\rightarrow|: & $V_1 \rightarrow V_2$ \\
  \verb|\dashedrightarrow|: & $V_1 \dashedrightarrow V_2$ \\
  \verb|\dashedrightarrow[4pt]|: & $V_1 \dashedrightarrow[4pt] V_2$
\end{tabular}
\end{document}

The above \dashedrightarrow[<len>] overwrites \rightarrow with a white \rule in the middle of the operator. The optional parameter provides a means to increase the dashed-ness, with a default of 2pt.