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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This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial L2 harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of L2 harmonic forms on complete hyperk...
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n=1 anq n be a holomorphic newform of weight k ≥ 2 relative to Γ1(N) acting on the upper half plane H. Suppose the coefficients an are all rational. When k = 2, a celebrated theorem of Shimura asserts that there corresponds an elliptic curve E over Q such that for all primes p N , ap = p + 1 − |E(Fp)|. Equivalently, there is, for every prime `, an `-adic representation ρ` of the absolute Galois...
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We study a class of two-dimensional N = (2, 2) sigma models called squashed toric sigma models, using their Gauged Linear Sigma Models (GLSM) description. These models are obtained by gauging the global U(1) symmetries of toric GLSMs and introducing a set of corresponding compensator superfields. The geometry of the resulting vacuum manifold is a deformation of the corresponding toric manifold ...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2001
ISSN: 0020-9910
DOI: 10.1007/pl00005802