K3 surfaces and related algebraic varieties

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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.