Modular forms on the moduli space of polarised K3 surfaces

We study the moduli space F_{2d} of polarised K3 surfaces of degree 2d. We compute all relations between Noether-Lefschetz divisors on these moduli spaces for d up to around 50. This leads to a very concrete description of the rational Picard group of F_{2d}. We show how to determine the coefficients of boundary components of relations in the rational Picard group, giving relations on a (toroidal) compactification of F_{2d}. We draw conclusions from this about the Kodaira dimension of F_{2d}, in many cases confirming earlier results by Gritsenko, Hulek and Sankaran, and in two cases giving a new result. This is an abridged version of the PhD thesis by the same author.