论文标题
环形b偏差和蒙格 - 安am措施
Toroidal b-divisors and Monge-Ampère measures
论文作者
论文摘要
我们将光滑和完整的曲折品种上的nef旋转孢子（Weil）b分离器的交点理论推广到光滑而完整的旋转嵌入情况。作为关键成分，我们显示了一个极限度量的存在，该量度是在附着在环形膜上的弱嵌入的有理锥形多面体空间上支持的，该空间是通过在多面体空间上通过热带相交理论定义的离散度量的限制而产生的。我们证明，可以将Nef环形卡地亚B型分子的交点理论连续扩展到nef toroidal weil b-divisors，并且可以将其程度计算为相对于此极限度量的积分。作为应用程序，我们表明希尔伯特 - 塞缪尔型公式适用于大型和nef toroidal weil b distivisors。
We generalize the intersection theory of nef toric (Weil) b-divisors on smooth and complete toric varieties to the case of smooth and complete toroidal embeddings. As a key ingredient we show the existence of a limit measure, supported on the weakly embedded 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 toroidal 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.
