论文标题
通过Galois封面分解Jacobians
Decomposing Jacobians via Galois covers
论文作者
论文摘要
令$ ϕ：\，x \ rightarrow y $为正属的两个代数曲线之间的（可能被分支）的覆盖率。我们开发的工具可以识别出$ ϕ $的prym品种，归功于同一基础，作为商曲线$ c $的雅各布，在$ ϕ $的Galois封闭中，具有精心选择的地图$ y \ rightarrow \ rightarrow \ mathbb {p}^1 $。这种方法使我们能够根据我们所知道的雅各布式来恢复所有先前获得的Prym品种的描述，此外还产生了新的应用。我们还发现其中一些新案例的代数方程，其中包括$ x $的属$ 3 $，$ y $具有$ 1 $ $ 1 $，而$ ϕ $是$ 3 $地图，$ 3 $地图完全被$ 2 $点分配。
Let $ϕ:\,X\rightarrow Y$ be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of $ϕ$, up to isogeny, as the Jacobian of a quotient curve $C$ in the Galois closure of the composition of $ϕ$ with a well-chosen map $Y\rightarrow \mathbb{P}^1$. This method allows us to recover all previously obtained descriptions of a Prym variety in terms of a Jacobian that are known to us, besides yielding new applications. We also find algebraic equations for some of these new cases, including one where $X$ has genus $3$, $Y$ has genus $1$ and $ϕ$ is a degree $3$ map totally ramified over $2$ points.
