第一类Koras-Russell三重自同构群
Automorphism groups of Koras-Russell threefolds of the first kind
摘要：
Koras-Russell三重曲面是仿射复四维空间中一类与仿射三重空间不代数同构的光滑可收缩复超曲面。其中一个重要的例子是三次罗素三倍，由方程x^2y+z^2+t^3+x=0定义。在A的前一篇文章中，Dubouloz，P. M. Poloni和作者，研究了Russell三次三重体的自同构群.特别地，证明了这个超曲面的所有自同构都扩展到周围空间的自同构。这有几个有趣的结果，包括可以找到另一个与罗素三次同构的超曲面，但这两个超曲面是不等价的。在本文中，我们将讨论如何将这些结果推广到第一类Koras-Russell三重类。
英文摘要：
Koras-Russell threefolds are certain smooth contractible complex hypersurfaces in affine complex four-space which are not algebraically isomorphic to affine three-space. One of the important examples is the cubic Russell threefold, defined by the equation x^2y+z^2+t^3+x=0. In a previous article by A. Dubouloz, P.M. Poloni and the author, 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
