Mixed mock modularity of special divisors

TL;DR

This paper demonstrates that the generating series of special divisors in certain Shimura varieties forms a mixed mock modular form, providing an explicit completion via theta series and using intersection theory at the boundary.

Contribution

It establishes the mixed mock modularity of special divisors' generating series and constructs an explicit theta series completion.

Findings

Generating series are mixed mock modular forms.

Explicit completion via theta series associated to rays.

Proof uses intersection theory at the boundary.

Abstract

We prove that the generating series of special divisors in toroidal compactifications of orthogonal Shimura varieties is a mixed mock modular form. More precisely, we find an explicit completion using theta series associated to rays in the cone decomposition. The proof relies on intersection theory at the boundary of the Shimura variety.