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arXiv · 2610.25538

Heights of small CM cycles on Unitary Shimura Varieties

Ziqi Guo
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Abstract

We compute the heights of small CM cycles on unitary Shimura varieties for general choices of the one-dimensional Hermitian subspace $W$ defining the embedding. The formula contains the logarithmic derivative of a quadratic Hecke $L$-function and explicit local terms depending on the choice of $W$. We prove this formula and an arithmetic Siegel--Weil identity by comparing the holomorphic projection of a mixed theta--Eisenstein derivative with arithmetic intersections of special divisors.

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Ziqi Guo. 2026-10-18. Heights of small CM cycles on Unitary Shimura Varieties. https://arxiv.org/abs/2610.25538

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