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

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

2006-11-10

arxiv.org/abs/math/0611307v1

Mathematics

Algebraic Geometry

Scientific paper

We define the notion of antispecial cycles on the Drinfeld upper half plane in analogy to the notion of special cycles defined by Kudla and Rapoport in their Inventiones paper. 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.

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