论文标题
特征零字段上的seshadri常数
Seshadri Constants Over Fields Of Characteristic Zero
论文作者
论文摘要
令$ x $为平稳的投射品种，定义在特征$ 0 $的字段$ k $上，让$ \ mathcal {l} $为$ k $定义的nef线束。我们证明，如果$ x \ in x $是$ k $ - 理性点，则seshadri constant $ε（x，\ mathcal {l}，x），x）$ over $ \ overline {k} $与$ k $超过$ k $相同。我们通过构建示例家族来表明，有一些全球seshadri常数$ε（x）$为零的品种。我们还证明了具有自然（和必要）假设的Seshadri曲线的结果。
Let $X$ be a smooth projective variety defined over a field $k$ of characteristic $0$ and let $\mathcal{L}$ be a nef line bundle defined over $k$. We prove that if $x\in X$ is a $k$-rational point then the Seshadri constant $ε(X, \mathcal{L}, x)$ over $\overline{k}$ is the same as that over $k$. We show, by constructing families of examples, that there are varieties whose global Seshadri constant $ε(X)$ is zero. We also prove a result on the existence of a Seshadri curve with a natural (and necessary) hypothesis.
