A Gross--Kohnen--Zagier Type Theorem for Higher-Codimensional Heegner Cycles

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.

52 pages, order of sections changed, updated and shortened

References in corpus (2)

• A $p$-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices
• Regularized Pairings of Meromorphic Modular Forms and Theta Lifts

Cited by in corpus (8)

• A $p$-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices
• Regularized Pairings of Meromorphic Modular Forms and Theta Lifts
• Shimura Lifts of Weakly Holomorphic Modular Forms
• Weight Changing Operators for Automorphic Forms on Grassmannians and Differential Properties of Certain Theta Lifts
• The Structure of Integral Parabolic Subgroups of Orthogonal Groups
• Orthogonal Eisenstein Series at Harmonic Points and Modular Forms of Singular Weight
• Heights of CM cycles and derivatives of L-series
• The $p$-adic variation of the Gross-Kohnen-Zagier theorem