FAMILIES OF GROUP ACTIONS, GENERIC ISOTRIVIALITY, AND LINEARIZATION

Our base field is the field ℂ of complex numbers. We study families of reductive group actions on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb A} $$\end{document}2 parametrized by curves and show that every faithful action of a non-finite reductive group on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb A} $$\end{document}3 is linearizable, i.e., G-isomorphic to a representation of G. The difficulties arise for non-connected groups G.