On degenerations of fiber spaces of curves of genus ≥ 2

In this note, we show that for surfaces admitting suitable fibrations, any given degeneration \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ {\cal X }/ {\mit \Delta} $\end{document} is bimeromorphic to a fiber space over a curve \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${ \cal Y}/ {\mit \Delta} $\end{document} and we apply this result to the study of the degenerate fiber.