具有54阶自同构群的三次曲面的周期
Periods of cubic surfaces with the automorphism group of order 54
摘要：
对于任何三次曲面，我们可以将一个由在这个三次曲面中分支的$\mathbb P^3$的三重覆盖给出的三次三重关联起来。D. Allcock，J. Carlson，and D.托莱多使用这种构造来定义三次曲面的周期图。对于某些特定的三次曲面，计算这种映射是很有趣的。本文计算了三次曲面由分支于光滑椭圆曲线上的$\mathbb P^2$的三重覆盖给出的情形。在这种情况下，可以通过对应的椭圆曲线的周期来表示周期。
英文摘要：
To any cubic surface, one can associate a cubic threefold given by a triple cover of $\mathbb P^3$ branched in this cubic surface. D. Allcock, J. Carlson, and D. Toledo used this construction to define the period map for cubic surfaces. It is interesting to calculate this map for some specific cubic surfaces. In this paper, we have calculated it in the case when the cubic surface is given by a triple covering of $\mathbb P^2$ branched in a smooth elliptic curve. In this case, the periods can be expressed through periods of the corresponding elliptic curve.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
