K3 and Enriques surfaces from the viewpoint of automorphisms

代数变异的自同构在变形条件下是不稳定的，并且深深依赖于它们的规则结构。因此他们的计算需要用到很多相关领域的结果，所以实际上对他们的研究可以说是非常有趣的。我们的研究主要集中在K3曲面和Enriques曲面上，这两个曲面目前已经得到了广泛的研究，并考虑了与它们的自同构相关的各种问题。具体地说，我们从一些K3曲面的自同构出发，从我们的观点研究了K3曲面上的Mordell-Weil格、log del Pezzo曲面和自由对合。

Automorphisms of algebraic varieties are not stable under deformations and depend deeply on their regular structure. Hence their computations need to use a number of results from related areas, so that in fact the research of them can be said to be very interesting. Our research focused on K3 surfaces and Enriques surfaces which had been extensively studied so far and considered various problems related to their automorphisms. Specifically, beginning with automorphisms of some K3 surfaces, we studied Mordell-Weil lattices, log del Pezzo surfaces and free involutions on K3 surfaces from our viewpoint.