Automorphism Groups of Koras-russell Threefolds of the First Kind
نویسنده
چکیده
Koras-Russell threefolds are certain smooth contractible complex hypersurfaces in A which are not algebraically isomorphic to A. One of the important examples is the cubic Russell threefold, defined by the equation xy + z + t + x = 0. In [D-MJ-P], the automorphism group of the Russell cubic threefold was studied. It was shown, in particular, that all automorphisms of this hypersurface extend to automorphisms of the ambient space. This has several interesting consequences, including the fact that one can find another hypersurface which is isomorphic to the Russell cubic, but such that the two hypersurfaces are inequivalent. In the present article, we will discuss how some of these results can be generalized to the class of Koras-Russell threefolds of the first kind.
منابع مشابه
Automorphism Groups of Koras-russell Threefolds of the Second Kind
We determine the automorphism groups of Koras-Russell threefolds of the second kind. In particular we show that these groups are semidirect products of two subgroups, one given by the multiplicative group and the other isomorphic to a polynomial ring in two variables with the addition law. We also show that these groups are generated by algebraic subgroups isomorphic to Gm and Ga.
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