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Mixed mock modularity of special divisors

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arxiv 2301.05982 v2 pith:XCDPHLAX submitted 2023-01-14 math.AG math.NT

Philip Engel , François Greer , Salim Tayou This is my paper · ORCID
classification math.AGmath.NT
keywords divisorsmixedmockseriesshimuraspecialassociatedboundary
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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.

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  1. The cohomological Kudla conjecture for unitary Shimura varieties

    math.NT 2025-07 conditional novelty 8.0 of 10

    The authors construct explicit boundary corrections making the Kudla-Millson generating series of special cycles on compactified unitary Shimura varieties a holomorphic Hermitian modular form for codimensions g ≤ n/2.

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