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We construct explicit generating series of arithmetic extensions of Kudla'sspecial divisors on integral models of unitary Shimura varieties over CM fieldswith arbitrary split levels and prove that they are modular forms valued in thearithmetic Chow groups. This provides a partial solution to Kudla's modularityproblem. The main ingredient in our construction is S.~Zhang's theory ofadmissible arithmetic divisors. The main ingredient in the proof is anarithmetic mixed Siegel-Weil formula.

Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)