论文标题
复杂的反射组和K3表面I
Complex reflection groups and K3 surfaces I
论文作者
论文摘要
我们在这里构建了许多K3表面的家族，可以通过等级四个复杂反射组的某些亚组作为代数表面的商来获得。我们在总共15个家庭中发现了最差的$ ade $ - 奇异性。特别是，我们将所有可以通过先前复合体反射组的派生子组获得的K3表面分类。我们通过使用嵌入这些表面的加权投影空间的几何形状以及Springer和Lehrer-Springer关于复杂反射组的性质的理论来证明我们的结果。该建筑概括了W. Barth和第二作者的先前建筑。
We construct here many families of K3 surfaces that one can obtain as quotients of algebraic surfaces by some subgroups of the rank four complex reflection groups. We find in total 15 families with at worst $ADE$--singularities. In particular we classify all the K3 surfaces that can be obtained as quotients by the derived subgroup of the previous complex reflection groups. We prove our results by using the geometry of the weighted projective spaces where these surfaces are embedded and the theory of Springer and Lehrer-Springer on properties of complex reflection groups. This construction generalizes a previous construction by W. Barth and the second author.
