TY - JOUR
T1 - A Gross–Kohnen–Zagier type theorem for higher-codimensional Heegner cycles
AU - Zemel, Shaul
N1 - Publisher Copyright:
© 2015, The Author(s).
PY - 2015/12/1
Y1 - 2015/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85020034750&partnerID=8YFLogxK
U2 - 10.1007/s40993-015-0025-3
DO - 10.1007/s40993-015-0025-3
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AN - SCOPUS:85020034750
SN - 2363-9555
VL - 1
JO - Research in Number Theory
JF - Research in Number Theory
IS - 1
M1 - 23
ER -