Maria Rosaria Pati: Special cycles on Kuga varieties over a Siegel threefold

Number Theory Seminar: Maria Rosaria Pati (University of Genova)

Special cycles on Kuga varieties over a Siegel threefold

We construct special cycles on the k-fold Kuga variety A^(k) over the Siegel threefold S_2(n) of level n, where k and n are positive integers with n > 2. These are cycles fibered over the points of Humbert surfaces in S_2(n). We prove that the generating series of the cohomology classes of these cycles is a modular form of weight k+5/2 and level Gamma subset of \tilde{SL}_2(Z) depending on n, for the metaplectic cover \tilde{SL}_2(Z) of SL_2. Our result generalizes to a higher weight setting previous works of Kudla and Millson on special cycles on Shimura varieties of orthogonal type.