Exotic affine space

In algebraic geometry, an exotic affine space is a complex algebraic variety that is diffeomorphic to for some n, but is not isomorphic as an algebraic variety to .[1][2][3] An example of an exotic is the Koras–Russell cubic threefold,[4] which is the subset of defined by the polynomial equation


  1. Snow, Dennis (2004), "The role of exotic affine spaces in the classification of homogeneous affine varieties", Algebraic Transformation Groups and Algebraic Varieties: Proceedings of the Conference Interesting Algebraic Varieties Arising in Algebraic Transformation Group Theory Held at the Erwin Schrödinger Institute, Vienna, October 22-26, 2001, Encyclopaedia of Mathematical Sciences, 132, Berlin: Springer, pp. 169–175, CiteSeerX, doi:10.1007/978-3-662-05652-3_9, ISBN 978-3-642-05875-2, MR 2090674.
  2. Freudenburg, G.; Russell, P. (2005), "Open problems in affine algebraic geometry", Affine algebraic geometry, Contemporary Mathematics, 369, Providence, RI: American Mathematical Society, pp. 1–30, doi:10.1090/conm/369/06801, ISBN 9780821834763, MR 2126651.
  3. Zaidenberg, Mikhail (1995-06-02). "On exotic algebraic structures on affine spaces". arXiv:alg-geom/9506005. Bibcode:1995alg.geom..6005Z. Cite journal requires |journal= (help)
  4. L Makar-Limanov (1996), "On the hypersurface in or a -like threefold which is not ", Israel J Math, 96 (2): 419–429, doi:10.1007/BF02937314

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.