具有环面作用的图超曲面及Aluffi的一个猜想

arXiv: Algebraic Geometry Pub Date : 2020-05-06 DOI:10.4310/CNTP.2021.v15.n3.a1

G. Denham, Delphine Pol, M. Schulze, U. Walther

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引用次数: 3

摘要

推广Muller-Stach和Westrich的星图，我们描述了一类图的关联超曲面具有非平凡环面作用的星图。对于这样的图，我们证明了相应的射影图超曲面补的欧拉特征为零。相反，我们也证明了所讨论的欧拉特征可以取任意整数值。这在很大程度上否定了Aluffi的一个猜想。

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Graph hypersurfaces with torus action and a conjecture of Aluffi

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.

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arXiv: Algebraic Geometry

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