We reprove and generalize a result proved by Yavin that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a connected linear solvable group acts, including all spherical varieties.

中文翻译：

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具有有限多个可解群轨道的簇的消失定理

我们反驳并推广了Yavin证明的结果，即非平凡一级局部系统中具有系数的环面簇的交交上同调群消失。我们证明了对于连通线性可解群作用的某一类簇（包括所有球形簇），类似的消失结果。