We generalize the intersection theory of nef toric (Weil) b-divisors on smooth and complete toric varieties to the case of nef b-divisors on complete varieties which are toroidal with respect to a snc divisor. As a key ingredient we show the existence of a limit measure, supported on a balanced rational conical polyhedral space attached to the toroidal embedding, which arises as a limit of discrete measures defined via tropical intersection theory on the polyhedral space. We prove that the intersection theory of nef Cartier b-divisors can be extended continuously to nef toroidal Weil b-divisors and that their degree can be computed as an integral with respect to this limit measure. As an application, we show that a Hilbert–Samuel type formula holds for big and nef toroidal Weil b-divisors.

我们将光滑和完全复曲面簇上的nef toric (Weil) b-因数的交集理论推广到关于snc因数呈环形的完整簇上的nef b-因数的情况。作为一个关键因素，我们展示了一个极限测度的存在，它由连接到环形嵌入的平衡合理圆锥多面体空间支持，这是通过多面体空间上的热带相交理论定义的离散测度的极限。我们证明了nef Cartier b-因数的相交理论可以连续扩展到nef toroidal Weil b-因数，并且它们的度数可以作为关于这个极限测度的积分来计算。作为一个应用，我们证明了 Hilbert-Samuel 型公式适用于大和中环 Weil b-除数。