Abstract
Let X be an algebraic variety isomorphic to the complement of a closed subvariety of dimension at most n − 3 in \( {\mathbbm{A}}_{\mathrm{k}}^n \). 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).
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