I'm writing a paper and I want to insert a figure that should occupy a whole page. Moreover, the figure has small details, so I want to reduce the margins in that page. On the other pages I'd like to use amsart margin settings. I reproduce my attempt below. The problem with that implementation is that the page is not "floating", so there is a big empty area in the preceding page.
\documentclass[10pt,letter]{amsart}
\usepackage[marginratio=1:1,height=584pt,width=360pt,tmargin=117pt]{geometry}
\usepackage{lipsum}
\usepackage{graphicx}
\usepackage[font=small]{caption}
\begin{document}
\title{A note}
\author{me}
\maketitle
\section{Introduction}
\lipsum
See Figure~\ref{fig.main}.
\newgeometry{right=5mm, left=5mm}
\begin{figure}
\centering
\includegraphics[width=\textwidth]{main_figure.pdf}
\caption{A huge figure.}\label{fig.main}
\end{figure}
\restoregeometry
\lipsum
\end{document}

geometrypackage. Instead, I'd leave the figure floating, with\begin{figure}[p]. I'd create a new dimension, say\mydimen, and set its size to\textwidthplus 10mm (the amount you've specified in your example with\newgeometry). Then in the figure, I'd insert the graphic with adjustments on the left and right:\noindent\hspace*{-5mm}\includegraphics{width=\mydimen]{...}\hspace{-5mm}The negative\hspaces should allow the graphic to overflow the width equally on each side without triggering an overfull hbox message. (Not tested.) – barbara beeton Nov 25 '19 at 20:17