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).

中文翻译：

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灵活变量中子变量等价的扩展

令X是\（{\ mathbbm {A}} _ {\ mathrm {k}} ^ n \）中维数最多为n  -3的闭合子变量的补集的同构代数变体。我们找到了一些条件，在这些条件下，X的两个封闭子变量的同构可以扩展为X的自同构。我们还研究了仿射二次曲面和SL（n，k）的子变量的相似问题。