Open Access

A Gross–Kohnen–Zagier type theorem for higher-codimensional Heegner cycles

Research in Number Theory20151:23

https://doi.org/10.1007/s40993-015-0025-3

Received: 22 April 2015

Accepted: 7 September 2015

Published: 7 December 2015

Abstract

We prove that the 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.