Toric varieties and modular forms
| dc.creator | Borisov, Lev A. | |
| dc.creator | Gunnells, Paul E. | |
| dc.date | 1999-08-26 | |
| dc.date.accessioned | 2026-07-07T05:30:30Z | |
| dc.date.available | 2026-07-07T05:30:30Z | |
| dc.description | Let $N\subset \RR^{r}$ be a lattice, and let $°\colon N \to \CC$ be a piecewise-linear function that is linear on the cones of a complete rational polyhedral fan. Under certain conditions on $°$, the data $(N,°)$ determines a function $f\colon {\HHH}\to \CC$ that is a holomorphic modular form of weight $r$ for the congruence subgroup $Γ_{1} (l) $. Moreover, by considering all possible pairs $(N ,°)$, we obtain a natural subring ${\TTT} (l)$ of modular forms with respect to $Γ_{1} (l) $. We construct an explicit set of generators for $\TTT (l)$, and show that ${\TTT} (l)$ is stable under the action of the Hecke operators. Finally, we relate ${\TTT} (l)$ to the Hirzebruch elliptic genera that are modular with respect to $Γ_{1} (l) $. | |
| dc.description | 27 pp., 1 figure, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/9908138 | |
| dc.identifier | http://arxiv.org/abs/math/9908138 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79011 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11F11, 11F25, 14M25 | |
| dc.title | Toric varieties and modular forms | |
| dc.type | text |