We present a formula to compute the Brasselet number of $$f:(Y,0)\rightarrow (\mathbb {C}, 0)$$ f : ( Y , 0 ) → ( C , 0 ) where $$Y\subset X$$ Y ⊂ X is a non-degenerate complete intersection in a toric variety X . As applications we establish several results concerning invariance of the Brasselet number for families of non-degenerate complete intersections. Moreover, when $$(X,0) = (\mathbb {C}^n,0)$$ ( X , 0 ) = ( C n , 0 ) we derive sufficient conditions to obtain the invariance of the Euler obstruction for families of complete intersections with an isolated singularity which are contained in X .

中文翻译：

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Brasselet 数和牛顿多边形

我们提出了一个公式来计算 $$f:(Y,0)\rightarrow (\mathbb {C}, 0)$$ f : ( Y , 0 ) → ( C , 0 ) 的 Brasselet 数，其中 $$Y\子集 X$$ Y ⊂ X 是复曲面簇 X 中的非退化完全交集。作为应用，我们建立了几个关于非退化完全交集族的 Brasselet 数不变性的结果。此外，当 $$(X,0) = (\mathbb {C}^n,0)$$ ( X , 0 ) = ( C n , 0 ) 我们推导出足够的条件来获得家庭的欧拉阻塞的不变性包含在 X 中的具有孤立奇点的完整交集。