  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.

Number Theory