Modularity of generating series of divisors on unitary Shimura varieties

We form generating series, valued in the Chow group and the arithmetic Chow group, of special divisors on the compactified integral model of a Shimura variety associated to a unitary group of signature pn ´1, 1q, and prove their modularity.The main ingredient in the proof is the calculation of vertical components appearing in the divisor of a Borcherds product on the integral model.