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Singular moduli of higher level and special cycles

Research in the Mathematical Sciences20152:16

Received: 15 February 2015

Accepted: 11 May 2015

Published: 17 August 2015


We describe the complex multiplication (CM) values of modular functions for \(\Gamma _0(N)\) whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply to Borcherds products of weight \(0\) for \(\Gamma _0(N)\). By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values.


  • Complex multiplication
  • CM values
  • Special cycles
  • Borcherds products