caa a22 4500 445862580 CHVBK 20180317145448.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00031-011-9146-5 doi (NATIONALLICENCE)springer-10.1007/s00031-011-9146-5 Poloni P.-M Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051, Basel, Switzerland aut Classification(s) of Danielewski hypersurfaces [Elektronische Daten] [P.-M. Poloni] The Danielewski hypersurfaces are the hypersurfaces X Q,n in $ {\mathbb{C}^3} $ defined by an equation of the form x n y = Q(x, z) where n ⩾ 1 and Q(x, z) is a polynomial such that Q(0, z) is of degree at least two. They were studied by many authors during the last twenty years. In the present article, we give their classification as algebraic varieties. We also give their classification up to automorphism of the ambient space. As a corollary, we obtain that every Danielewski hypersurface X Q,n with n ⩾ 2 admits at least two nonequivalent embeddings into $ {\mathbb{C}^3} $ . Springer Science+Business Media, LLC, 2011 Transformation Groups SP Birkhäuser Verlag Boston 16/2(2011-06-01), 579-597 1083-4362 16:2<579 2011 16 31 https://doi.org/10.1007/s00031-011-9146-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9146-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Poloni P.-M Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051, Basel, Switzerland aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/2(2011-06-01), 579-597 1083-4362 16:2<579 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer