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Displaying similar documents to “Abhyankar-Moh property and unique affine embeddings.”

Proof of the Knop conjecture

Ivan V. Losev (2009)

Annales de l’institut Fourier

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In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoid are equivariantly isomorphic. We also state and prove a uniqueness property for (not necessarily smooth) affine spherical varieties.

Local characterization of algebraic manifolds and characterization of components of the set S f

Zbigniew Jelonek (2000)

Annales Polonici Mathematici

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We show that every n-dimensional smooth algebraic variety X can be covered by Zariski open subsets U i which are isomorphic to closed smooth hypersurfaces in n + 1 . As an application we show that forevery (pure) n-1-dimensional ℂ-uniruled variety X m there is a generically-finite (even quasi-finite) polynomial mapping f : n m such that X S f . This gives (together with [3]) a full characterization of irreducible components of the set S f for generically-finite polynomial mappings f : n m .