18,458 research outputs found
Dwork families and -modules
A Dwork family is a one-parameter monomial deformation of a Fermat
hypersurface. In this paper we compute algebraically the invariant part of its
Gauss-Manin cohomology under the action of certain subgroup of automorphisms.
To achieve that goal we use the algebraic theory of -modules,
especially one-dimensional hypergeometric ones.Comment: 24 pages, final versio
Irregular Hodge filtration of some confluent hypergeometric systems
We determine the irregular Hodge filtration, as introduced by Sabbah, for the
purely irregular hypergeometric -modules. We obtain in particular
a formula for the irregular Hodge numbers of these systems. We use the
reduction of hypergeometric systems from GKZ-systems as well as comparison
results to Gauss-Manin systems of Laurent polynomials via Fourier-Laplace and
Radon transformations.Comment: 32 pages, final versio
Lagrangian 3-torus fibrations
We prove that Mark Gross' topological Calabi-Yau compactifications can be made into symplectic compactifications. To prove this we develop a method to construct singular Lagrangian 3-torus fibrations over certain a priori given integral affine manifolds with singularities, which we call simple. This produces pairs of compact symplectic 6-manifolds homeomorphic to mirror pairs of Calabi-Yau 3-folds together with Lagrangian fibrations whose underlying integral affine structures are dual
Crossed extensions of the corepresentation category of finite supergroup algebras
We present explicit examples finite tensor categories that are C_2-graded
extensions of the corepresentation category of certain finite-dimensional
non-semisimple Hopf algebras.Comment: 26 pages. An error in the product given in definition 4.7 was
correcte
Modular Invariant of Quantum Tori II: The Golden Mean
In our first article in this series ("Modular Invariant of Quantum Tori I:
Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of
quantum tori was defined. In this paper, we consider the case of the quantum
torus associated to the golden mean. We show that the modular invariant is
approximately 9538.249655644 by producing an explicit formula for it involving
weighted versions of the Rogers-Ramanujan functions
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