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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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Cite

BibTeXRIS
BibTeX
@misc{guo2026heights,
  title = {{Heights of small CM cycles on Unitary Shimura Varieties}},
  author = {Ziqi Guo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25538},
  eprint = {2610.25538},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25538},
}
RIS
TY  - UNPB
TI  - Heights of small CM cycles on Unitary Shimura Varieties
AU  - Ziqi Guo
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25538
UR  - https://arxiv.org/abs/2610.25538
AB  - 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.
ER  -