论文标题
非架构的Metrized NEF线束
Non-Archimedean volumes of metrized nef line bundles
论文作者
论文摘要
让$ l $成为适当的，几何降低的方案$ x $的线捆绑包，而不是估值的非Archimedean field $ k $。粗略地说，关于$ l $的伯科维奇分析的连续度量标准的非架构数量衡量了$ l $的张量量量的小部分空间的渐近生长。对于Zhang的$ L $的连续半阳性度量，我们首先证明非架构的卷与能量一致。这样的半阳性度量的存在，即$ l $是nef。第二个结果是，在任何半阳性连续度量标准下，非架构的体积都是可区分的。当$ L $充足的情况下，这些结果是已知的，本文的目的是将其推广到NEF案例。该方法基于对$ k $的（可能是非核）评估环（可能是非noetherian）评估环上有限呈现的扭转模块的详细研究。
Let $L$ be a line bundle on a proper, geometrically reduced scheme $X$ over a non-trivially valued non-Archimedean field $K$. Roughly speaking, the non-Archimedean volume of a continuous metric on the Berkovich analytification of $L$ measures the asymptotic growth of the space of small sections of tensor powers of $L$. For a continuous semipositive metric on $L$ in the sense of Zhang, we show first that the non-Archimedean volume agrees with the energy. The existence of such a semipositive metric yields that $L$ is nef. A second result is that the non-Archimedean volume is differentiable at any semipositive continuous metric. These results are known when $L$ is ample, and the purpose of this paper is to generalize them to the nef case. The method is based on a detailed study of the content and the volume of a finitely presented torsion module over the (possibly non-noetherian) valuation ring of $K$.
