与Klein曲面相关的某些纤维化的非理性
Non-rationality of some fibrations associated to Klein surfaces
摘要：
我们研究多项式纤维化诱导的方程的克莱因曲面作为商的有限线性群的自同构的平面，这些表面的类型A，D，E，对应于他们的奇点。多项式纤维化的一般纤维是在直线的函数域上定义的曲面。我们证明了它在情形D，E中是不合理的，尽管它在情形A中是明显合理的。还描述了克莱因曲面的自同构群，并且在情况D、E中是线性的且具有有限维度;在情况A中，该结果显然是错误的。
英文摘要：
We study the polynomial fibration induced by the equation of the Klein surfaces obtained as quotient of finite linear groups of automorphisms of the plane; this surfaces are of type A, D, E, corresponding to their singularities. The generic fibre of the polynomial fibration is a surface defined over the function field of the line. We proved that it is not rational in cases D, E, although it is obviously rational in the case A. The group of automorphisms of the Klein surfaces is also described, and is linear and of finite dimension in cases D, E; this result being obviously false in case A.
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