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Toroidal b-divisors and Monge–Ampère measures
Mathematische Zeitschrift ( IF 1.0 ) Pub Date : 2021-06-24 , DOI: 10.1007/s00209-021-02789-5
Ana María Botero , José Ignacio Burgos Gil

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.



中文翻译:

环形 b-除数和 Monge-Ampère 测度

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。

更新日期:2021-06-24
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