On Endomorphism of Algebraic Varieties
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classification
math.AG
keywords
algebraicclosedendomorphismautomorphismcomplementinjectiveprovesubvariety
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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 $2$, is an automorphism.
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