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

Research in Number Theory20151:23

  • Received: 22 April 2015
  • Accepted: 7 September 2015
  • Published:


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.


  • Modular Form
  • Cusp Form
  • Automorphic Form
  • Hodge Structure
  • Abelian Surface