Modularity of generating series of divisors on unitary Shimura varieties

TL;DR

This paper proves the modularity of generating series of special divisors on a compactified integral model of a unitary Shimura variety, involving Chow groups and Borcherds products.

Contribution

It establishes the modularity of generating series of divisors valued in Chow and arithmetic Chow groups on unitary Shimura varieties, with detailed calculations of vertical components.

Findings

Generated series are modular forms.

Vertical components are explicitly calculated.

Results connect special divisors with automorphic forms.

Abstract

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