论文标题
盖洛伊斯封闭5倍覆盖和分解的雅各比安
Galois closure of a 5-fold covering and decomposition of its Jacobian
论文作者
论文摘要
对于紧凑的riemann表面之间的任意5倍分支的覆盖率，根据地图的分支数据确定了每个可能的galois闭合；也就是说，覆盖地图的分支。由于作用于Galois闭合的群体也对覆盖面的雅各布品种作用，因此我们用雅各比式和prym品种的中间覆盖物的jacobian和prym品种描述了其组代数分解。分解中每个阿贝尔品种的尺寸和诱导的极化是根据覆盖地图的后果数据计算的。
For an arbitrary 5-fold ramified covering between compact Riemann surfaces, every possible Galois closure is determined in terms of the ramification data of the map; namely, the ramification divisor of the covering map. Since the group that acts on the Galois closure also acts on the Jacobian variety of the covering surface, we describe its group algebra decomposition in terms of the Jacobian and Prym varieties of the intermediate coverings of the Galois closure. The dimension and induced polarization of each abelian variety in the decomposition is computed in terms of the ramification data of the covering map.
