Complex multiplication cycles and Kudla-Rapoport divisors


We study the intersections of special cycles on a unitary Shimura variety of signature $(n-1,1)$ and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of conjectures of Kudla and suggest a Gross-Zagier theorem for unitary Shimura varieties.


Benjamin Howard

Department of Mathematics, Boston College, Chestnut Hill, MA 92467