论文标题
Galois子空间，用于光滑的投影曲线
Galois subspaces for smooth projective curves
论文作者
论文摘要
给定平滑的投射曲线$ x $属属$ g \ geq1 $纳入$ \ mathbb {p}^n $中，我们研究了$ \ mathbb {p}^n $的线性子空间的座位，以使得与embedding of empedding ass y Mathb y Marthbbbbb {p}^n $ codimension 2的codimension 2的预测，可提供palois $ x $ $ x $ x $ $ x $对于$ g \ geq2 $的属，我们证明该基因座是一个光滑的投射品种，其组件具有同构与投影空间的同构。如果$ g = 1 $且嵌入由完整的线性系统给出，我们证明该基因座也是一个光滑的投射品种，其正维成分对椭圆曲线的od the tale套件的构成捆绑符号是同构的，我们明确地描述了这些组件。
Given an embedding of a smooth projective curve $X$ of genus $g\geq1$ into $\mathbb{P}^N$, we study the locus of linear subspaces of $\mathbb{P}^N$ of codimension 2 such that projection from said subspace, composed with the embedding, gives a Galois morphism $X\to\mathbb{P}^1$. For genus $g\geq2$ we prove that this locus is a smooth projective variety with components isomorphic to projective spaces. If $g=1$ and the embedding is given by a complete linear system, we prove that this locus is also a smooth projective variety whose positive-dimensional components are isomorphic to projective bundles over étale quotients of the elliptic curve, and we describe these components explicitly.
