论文标题
klein四个盖子的全态差异
Holomorphic differentials of Klein four covers
论文作者
论文摘要
令$ k $为特征两个的代数封闭字段，让$ g $是同构为$ \ m athbb {z}/2 \ times \ times \ mathbb {z}/2 $。假设$ x $是$ k $的一条平稳的投影不可约的曲线，并带有忠实的$ g $ Action，并假设盖上$ x \ to x/g $被完全损坏，从某种意义上说，它被损坏了并且每个分支点都被完全分配。我们研究了$ x $的封闭点的下降较低的分支小组，确定了不可塑性$ kg $ - 模块的同构类型，以及它们作为空间的直接总和$ \ mathrm {h}^0（H}^0（x，x，ω__{x/k}）$ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x。在$ x/g = \ mathbb {p}^1_k $的情况下，我们完全确定$ \ mathrm {h}^0的分解（x，x，ω__{x/k}）$直接纳入$ kg $ -modules的直接总和。此外，我们表明，当直接汇总属于无限的非晶状体不可兼容$ kg $ kg $模块的无限列表中，实际上发生的不可塑性$ kg $模型的同构类别的同构类别的同构类别$ kg $ kg $ kg $ kg $ kg $ kg $ kg $ kg $ kg $ kg $ kg $ kg $ kg $ sode，特别是，我们的结果表明[14，定理6.4]是不正确的。
Let $k$ be an algebraically closed field of characteristic two, and let $G$ be isomorphic to $\mathbb{Z}/2\times\mathbb{Z}/2$. Suppose $X$ is a smooth projective irreducible curve over $k$ with a faithful $G$-action, and assume that the cover $X\to X/G$ is totally ramified, in the sense that it is ramified and every branch point is totally ramified. We study to what extent the lower ramification groups of the closed points of $X$ determine the isomorphism types of the indecomposable $kG$-modules and the multiplicities with which they occur as direct summands of the space $\mathrm{H}^0(X,Ω_{X/k})$ of holomorphic differentials of $X$ over $k$. In the case when $X/G=\mathbb{P}^1_k$, we completely determine the decomposition of $\mathrm{H}^0(X,Ω_{X/k})$ into a direct sum of indecomposable $kG$-modules. Moreover, we show that the isomorphism classes of indecomposable $kG$-modules that actually occur as direct summands belong to an infinite list of non-isomorphic indecomposable $kG$-modules that contain modules of arbitrarily large $k$-dimension. In particular, our results show that [14, Theorem 6.4] is incorrect.
