On Endomorphism of Algebraic Varieties
Nilkantha Das

TL;DR
The paper proves that certain injective endomorphisms of algebraic varieties over characteristic zero fields are actually automorphisms, especially when injectivity holds outside a small subvariety.
Contribution
It establishes conditions under which endomorphisms become automorphisms, extending previous results to broader classes of algebraic varieties.
Findings
Injective endomorphisms outside a closed subvariety are automorphisms over characteristic zero fields.
Injectivity outside a codimension at least 2 subvariety implies automorphism for complex algebraic varieties.
Results generalize known automorphism criteria for algebraic varieties.
Abstract
We prove that a quasi-finite endomorphism of an algebraic variety over an algebraically closed field of characteristic zero, that is injective on the complement of a closed subvariety, is an automorphism. We also prove that an endomorphism of complex algebraic variety that is injective on the complement of a closed subvariety of codimension at least , is an automorphism.
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Taxonomy
TopicsAdvanced Algebra and Logic
