Open Access

Singular moduli of higher level and special cycles

Research in the Mathematical Sciences20152:16

https://doi.org/10.1186/s40687-015-0030-0

Received: 15 February 2015

Accepted: 11 May 2015

Published: 17 August 2015

Abstract

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.

Keywords

Complex multiplication CM values Special cycles Borcherds products