EXTENSIONS OF ISOMORPHISMS OF SUBVARIETIES IN FLEXIBLE VARIETIES

Let X be an algebraic variety isomorphic to the complement of a closed subvariety of dimension at most n − 3 in Akn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbbm{A}}_{\mathrm{k}}^n $$\end{document}. We find some conditions under which an isomorphism of two closed subvarieties of X can be extended to an automorphism of X. We also study the similar problem for subvarieties of affine quadrics and SL(n, k).