Singular moduli of higher level and special cycles

Abstract

We describe the complex multiplication (CM) values of modular functions for $\hat{I}{“}_0(N)$ 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 $\hat{I}{“}_0(N)$. By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values.

25 pages; Research in the Mathematical Sciences (2015, to appear); Fixed internal references and corrected some typos