A Gross--Kohnen--Zagier Type Theorem for Higher-Codimensional Heegner Cycles
Number Theory
2020-08-12 v2
Abstract
We prove that Heegner cycles of codimension m+1 inside Kuga-Sato type varieties of dimension 2m+1 are coefficients of modular forms of weight 3/2+m in the appropriate quotient group. The main technical tool for generating the necessary relations is a Borcherds style theta lift with polynomials. We also show how this lift defines a new singular Shimura-type correspondence from weakly holomorphic modular forms of weight 1/2-m to meromorphic modular forms of weight 2m+2.
Cite
@article{arxiv.1306.6463,
title = {A Gross--Kohnen--Zagier Type Theorem for Higher-Codimensional Heegner Cycles},
author = {Shaul Zemel},
journal= {arXiv preprint arXiv:1306.6463},
year = {2020}
}
Comments
52 pages, order of sections changed, updated and shortened