A celebrated result of Hirzebruch and Zagier states that th e generating series of Hirzebruch-Zagier divisors on a Hilbert modular sur face is an elliptic modular form with values in the cohomology. We discuss some generalizations and applications of this result. In particular\, we report on recent joint work with B. Howard\, S. Kudla\, M. Rapoport\, and T. Yang\, in which we prove an analogue for special divisors on integral m odels of ball quotients. In this setting the generating series takes value s in an arithmetic Chow group in the sense of Arakelov geometry. If time p ermits\, we address some applications to arithmetic theta lifts and the Co lmez conjecture.

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