## Abstract

Let W ⊂ ℝ^{r} be a lattice, and let deg : N → ℂ be a piecewise-linear function that is linear on the cones of a complete rational polyhedral fan. Under certain conditions on deg, the data (N, deg) determines a function f : Heng hooktop sign → ℂ that is a holomorphic modular form of weight r for the congruence subgroup Γ_{1}(l). Moreover, by considering all possible pairs (N, deg), we obtain a natural subring Script T sign (l) of modular forms with respect to Γ_{1}(l). We construct an explicit set of generators for Script T sign (l), and show that Script T sign (l) is stable under the action of the Hecke operators. Finally, we relate Script T sign (l) to the Hirzebruch elliptic genera that are modular with respect to Γ_{1}(l).

Original language | English (US) |
---|---|

Pages (from-to) | 297-325 |

Number of pages | 29 |

Journal | Inventiones Mathematicae |

Volume | 144 |

Issue number | 2 |

DOIs | |

State | Published - 2001 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)