m at h . N T ] 2 6 A ug 1 99 9 TORIC VARIETIES AND MODULAR FORMS
نویسنده
چکیده
Let N ⊂ Rr 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 : H → C that is a holomorphic modular form of weight r for the congruence subgroup Γ1(l). Moreover, by considering all possible pairs (N, deg), we obtain a natural subring T (l) of modular forms with respect to Γ1(l). We construct an explicit set of generators for T (l), and show that T (l) is stable under the action of the Hecke operators. Finally, we relate T (l) to the Hirzebruch elliptic genera that are modular with respect to Γ1(l).
منابع مشابه
On Toric Varieties and Modular Forms
Let M∗(l) = M∗(Γ1(l),C) be the ring of holomorphic modular forms on Γ1(l). In this talk we use the combinatorics of complete toric varieties to construct a subring T∗(l) ⊂ M∗(l), the subring of toric modular forms (§2). This is a natural subring, in the sense that it behaves nicely with respect to natural operations on M∗(l) (namely, Hecke operators, Fricke involution, and the theory of oldform...
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