Analytic extensions of algebraic isomorphisms
Shulim Kaliman

TL;DR
The paper proves that algebraic isomorphisms between certain affine subvarieties of complex space can be extended to holomorphic automorphisms of the ambient space, under specific dimension conditions.
Contribution
It establishes conditions under which algebraic isomorphisms extend to holomorphic automorphisms, including for curves in higher dimensions.
Findings
Extension of isomorphisms to automorphisms under dimension constraints
Existence of extensions for curve isomorphisms in all dimensions ≥ 3
Extension results hold even when tangent space dimension equals ambient space dimension
Abstract
Let be an isomorphism of closed affine algebraic subvarities of such that . We prove that can be extended to a holomorphic automorphism of . Furthermore, when is an isomorphism of curves such an extension exists for every even when .
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Meromorphic and Entire Functions
