# underline in a part of a section title in amsart

I want to use math symbols including underline (e.g. $\underline{R}_{H,V}$) in a section title in a document in amsart documentclass with table of contents. So I typed (roughly)

\documentclass{amsart}
\begin{document}
\tableofcontents

\section{The functor ${\underline{R}}_{H,V}$}

\end{document}

If I compile this file, I get the section title as wanted, but without the underline in the table of contents. If I compile once more, I get the following error message:

Missing } inserted
}
...elax }_{H,V}\$

I checked this site and found advices suggesting to use sectsty or titlesec packages. But they seem to be useful only when you want to underline the whole section title in article documentclass. Can anybody help?

-