We develop splitting techniques to study the Lyubeznik numbers of cover ideals of graphs which allow us to describe them for large families of graphs including forests, cycles, wheels and cactus graphs. More generally, we are able to compute all the Bass numbers and the shape of the injective resolution of local cohomology modules by considering the connected components of all the induced subgraphs. Indeed, our method gives us a very simple criterion for the vanishing of these local cohomology modules in terms of the number of connected components of the induced subgraphs.

中文翻译：

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图的覆盖理想的局部同调的低音数

我们开发了分割技术来研究图的覆盖理想值的Lyubeznik数，这使我们能够针对森林，循环图，轮图和仙人掌图等大图族描述它们。更一般而言，我们能够通过考虑所有诱导子图的连接分量来计算所有低音数和局部同调模块的内射分辨率的形状。确实，我们的方法为我们提供了一个非常简单的准则，可以根据诱导子图的连接部分数量来消除这些局部同调模块。