论文标题
用圆环动作和猜想的Aluffi的图形高度曲面
Graph hypersurfaces with torus action and a conjecture of Aluffi
论文作者
论文摘要
概括了Müller-Stach和Westrich的星形图，我们描述了一类图形，其相关图超表面配备了非平凡的圆环动作。对于此类图，我们表明相应的射影图超表面补体的Euler特性为零。相比之下，我们还表明，所讨论的欧拉特征可以为合适的图提供任何整数值。从强烈的意义上讲，这反驳了Aluffi的猜想。
Generalizing the star graphs of Müller-Stach and Westrich, we describe a class of graphs whose associated graph hypersurface is equipped with a non-trivial torus action. For such graphs, we show that the Euler characteristic of the corresponding projective graph hypersurface complement is zero. In contrast, we also show that the Euler characteristic in question can take any integer value for a suitable graph. This disproves a conjecture of Aluffi in a strong sense.
