Antispecial cycles on the Drinfeld upper half plane and degenerate Hirzebruch–Zagier cycles

We define the notion of antispecial cycles on the Drinfeld upper half plane in analogy to the notion of special cycles in Kudla and Rapoport (Invent Math 142:153–223, 2000). We determine equations for antispecial cycles and calculate the intersection multiplicity of two antispecial cycles. The result is applied to calculate the intersection multiplicity of certain degenerate Hirzebruch–Zagier cycles. Finally we compare this intersection multiplicity to certain representation densities.