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Subjects
14-XX Algebraic geometry
14Exx Birational geometry
14E05 Rational and birational maps

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Injective endomorphisms of algebraic and analytic sets

Sławomir Cynk, Kamil Rusek (1991)

Annales Polonici Mathematici

We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.

Injective endomorphisms of algebraic varieties.

Krzysztof Jan Nowak (1994)

Mathematische Annalen

Intrinsic Measures of Compact Complex Manifolds.

Shing Tung Yau (1974)

Mathematische Annalen

Involutive birational transformations of arbitrary complexity in Euclidean spaces

Zdeněk Dušek, Oldřich Kowalski (2013)

Commentationes Mathematicae Universitatis Carolinae

A broad family of involutive birational transformations of an open dense subset of $ℝ^{n}$ onto itself is constructed explicitly. Examples with arbitrarily high complexity are presented. Construction of birational transformations such that $φ^{k} = Id$ for a fixed integer $k > 2$ is also presented.

Currently displaying 1 – 4 of 4

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