K3 surfaces and related algebraic varieties

通过编写各种计算机程序进行格的计算研究，并将其应用于K3曲面上的代数圈格（或相关的代数簇），我们得到了许多几何结果。通过引入Z-分裂曲线的概念，对6次简单平面曲线的Zurski对进行了分类，并描述了它们的邻接关系。对于给定的复代数曲面，我们给出了一个确定代数曲线格在拓扑圈格中的连续性的算法。

By writing various computer programs for the computational research of lattices and applying them to lattices of algebraic cycles on K3 surfaces(or related algebraic varieties), we obtained many geometric consequences. In particular, we classified the Zariski pairs of simple plane curves of degree 6 by introducing a notion of Z-splitting curves, and described their adjacency relations. We also presented an algorithm to determine the primitivity of a lattice of algebraic curves in the lattice of topological cycles for a given complex algebraic surface.