Graph hypersurfaces with torus action and a conjecture of Aluffi

Graph hypersurfaces with torus action and a conjecture of Aluffi
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DOI：
10.4310/cntp.2021.v15.n3.a1
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发表时间：
2020-05
期刊：
arXiv: Algebraic Geometry
影响因子：
--
通讯作者：
G. Denham;Delphine Pol;M. Schulze;U. Walther
G. Denham;Delphine Pol;M. Schulze;U. Walther
中科院分区：
其他
文献类型：
--
作者：
G. Denham;Delphine Pol;M. Schulze;U. Walther

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推广了Muller-Stach和Westrich的星星图，刻画了一类图的超曲面具有非平凡环面作用的图.对于这样的图，我们证明了相应的投影图超曲面补的欧拉特征是零。相反，我们还表明，欧拉特征的问题可以采取任何整数值的一个合适的图。这在很强的意义上否定了一个猜想。
Generalizing the star graphs of Muller-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.