论文标题
$ 12 $锥形和广义kummer表面的特殊配置
A special configuration of $12$ conics and generalized Kummer surfaces
论文作者
论文摘要
通过命令3的符号自动形态获得的广义Kummer表面$ x $作为Abelian表面的商，其中包含$ 9 \ Mathbf {a} _ {2} $ - $（2）$ - curves的配置。这样的配置扮演着$ 16 \ mathbf {a} _ {1} $ - 通常的kummer表面的配置。在本文中，我们构建了$ 9 $其他这样的$ 9 \ Mathbf {a} _ {2} $ - 在与立方曲线的六曲线上分支的平面双盖相关的广义kummer表面上的配置。新的$ 9 \ mathbf {a} _ {2} $ - 配置是通过取下一定的$ 12 $锥形的回调，这些配置在分支曲线方面处于特殊位置，再加上一些奇异的四分之一曲线。然后，我们构建了K3表面的一些自动形态，将一种配置发送到另一种配置。我们还提供各种$ x $的型号以及其天然椭圆铅笔的通用纤维。
A generalized Kummer surface $X$ obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 contains a $9\mathbf{A}_{2}$-configuration of $(-2)$-curves. Such a configuration plays the role of the $16\mathbf{A}_{1}$-configurations for usual Kummer surfaces. In this paper we construct $9$ other such $9\mathbf{A}_{2}$-configurations on the generalized Kummer surface associated to the double cover of the plane branched over the sextic dual curve of a cubic curve. The new $9\mathbf{A}_{2}$-configurations are obtained by taking the pullback of a certain configuration of $12$ conics which are in special position with respect to the branch curve, plus some singular quartic curves. We then construct some automorphisms of the K3 surface sending one configuration to another. We also give various models of $X$ and of the generic fiber of its natural elliptic pencil.
