More aesthetic (perhaps shallower) superscript check symbol

Question

The standard way to produce a superscript check mark in latex would be something like

$\mathcal{E}^{\vee}$

(this is a notation often used for the dual of a locally free sheaf $\mathcal{E}$.) An alternative using the amsxtra package would be

$\mathcal{E}\spcheck$

but this looks exactly the same. If I correctly understand, it's really just a shortcut for the former code.

Personally, I find this version of a superscript check unaesthetic. In particular, I think it should be shallower. I could probably go searching in comprehensive symbol lists for something I like better, but I believe I'll end up with a better solution if I ask here.

What is a good way to produce a more aesthetic (and in particular, shallower) version of a superscript check mark in math mode?

Answer 1

this is probably heresy, but you might consider using the \check accent over "nothing":

the vertical position can be adjusted by inserting a zero-width \vrule as the "nothing":

\[
   \mathcal{E}\,\check{} \quad
   \mathcal{E}\,\check{\vrule height1.3ex width0pt}
\]

Answer 2

How about a macro \smvee (short for "small vee"), implemented in the following MWE:

\documentclass[12pt]{article}
\newcommand\smvee{\raise0.9ex\hbox{$\scriptscriptstyle\vee$}}
\begin{document}
$\mathcal{E}^{\vee}$, $\mathcal{E}\smvee$
\end{document}

Addendum: Relative to the "ordinary" \vee in a superscript position, the height of the \smvee symbol is about 30% smaller. The amount of the vertical displacement in the macro (0.9ex) was chosen so that the upper endpoints of the (small) vee line up with the upper endpoint of the \mathcal{E} character. You may wish to adjust this to suit your personal preferences.

Answer 3

The amssymb package offers \checkmark that has "varying thickness" and "a tiny bit of curvature":

\documentclass{article}
\usepackage{amssymb,amsxtra}% http://ctan.org/pkg/{amssymb,amsxtra}
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
\newcommand*{\dual}[1][E]{\mathcal{#1}^{\scalebox{.5}{\checkmark}}}%
\begin{document}
$\mathcal{E}^{\vee}$ \par
$\mathcal{E}\spcheck$ \par
$\dual$ \par
$\dual[G]$
\end{document}

From the above MWE, you only need graphicx and amssymb.

Answer 4

Adjust \raisebox and \scalebox arguments as needed. The extra $ around the \vee look unnecessary, but they're actually required.

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}

\begin{document}
$\mathcal{E}^{\vee}$

$\mathcal{E}^{\raisebox{0.5ex}{\scalebox{0.5}[0.25]{$\vee$}}}$
\end{document}