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arXiv · 1710.05580

Generating series of intersection volumes of special cycles on unitary Shimura varieties

Zavosh Amir-Khosravi
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Abstract

We form a generating series of regularized volumes of intersections of special cycles on a non-compact unitary Shimura variety with a fixed base change cycle. We show that it is a Hilbert modular form by identifying it with a theta integral, which we show converges even though the parameters lie outside the classical convergence range of Weil. By applying the regularized Siegel-Weil formulas of Ichino and Gan-Qiu-Takeda, we show the modular form is the restriction of a hermitian modular form of degree n related to Siegel Eisenstein series on U(n,n). An essential fact used is a computation showing the Kudla-Millson Schwartz function vanishes under the Ikeda map.

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Zavosh Amir-Khosravi. 2017-10-16. Generating series of intersection volumes of special cycles on unitary Shimura varieties. https://arxiv.org/abs/1710.05580

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