Extensions of isomorphisms of subvarieties in flexile varieties

Shulim Kaliman

Extensions of isomorphisms of subvarieties in flexile varieties

Algebraic Geometry 2018-12-03 v7

Authors: Shulim Kaliman

Abstract

Let $X$ be a quasi-affine algebraic variety isomorphic to the complement of a closed subvariety of dimension at most $n-3$ in $\C^n$ . We find some conditions under which an isomorphism of two closed subvarieties of $X$ can be extended to an automorphism of $X$ .

Keywords

quasi-affine varieties isomorphism extension automorphisms flexible varieties algebraic geometry

Cite

@article{arxiv.1703.08461,
  title  = {Extensions of isomorphisms of subvarieties in flexile varieties},
  author = {Shulim Kaliman},
  journal= {arXiv preprint arXiv:1703.08461},
  year   = {2018}
}

Comments

In this version (March 2018) there are new sections with extra results about the extension problem in SL(n). In version 3 add two sections 8 and 9 concerning the extension problem for affine quadrics and SL (n). The first seven sections are essentially the same. In version 4 there are small corrections in Proposition 6.7 and Remark 6.8

Extensions of isomorphisms of subvarieties in flexile varieties

Abstract

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