The Griffiths group of a general Calabi-Yau threefold is not finitely generated

The Griffiths Group of a General Calabi-yau Threefold Is Not Finitely Generated

Fn−k+1H 2n−2k+1(X)∼= F n−k+1A2n−2k+1(X)c dFn−k+1A2n−2k(X) . If (Zt )t∈C is a flat family of codimension k algebraic cycles on X parametrized by a smooth irreducible curve C, the map t → kX(Zt − Z0) factors through a homomorphism from the Jacobian J (C) to J 2k−1(X), and one can show that the image of this morphism is a complex subtorus of J 2k−1(X) whose tangent space is contained in Hk−1,k(X) ...

Modularity of a Certain Calabi-yau Threefold

The Langlands program predicts that certain Calabi-Yau threefolds are modular in the sense that their L-series correspond to the Mellin transforms of weight 4 newforms. Here we prove that the L-function of the threefold given by P4 i=1(xi + x −1 i ) = 0 is η 4(2z)η4(4z), the unique normalized eigenform in S4(Γ0(8)).

A Modular Non-Rigid Calabi-Yau Threefold

We construct an algebraic variety by resolving singularities of a quintic Calabi-Yau threefold. The middle cohomology of the threefold is shown to contain a piece coming from a pair of elliptic surfaces. The resulting quotient is a two-dimensional Galois representation. By using the Lefschetz fixed-point theorem in étale cohomology and counting points on the variety over finite fields, this Gal...

Form field theory on Calabi-Yau threefold

We show how the natural Abelian duality of 2 and 3-form gravity theories in 7-dimensional manifold CY3 × S leads to an S-duality between 2 and 3-form theories on simply connected CY3. The massless sector of the 2-form field theory on CY3 corresponds to the A model string field theory. We discuss the complex structure independence of the 2 form theory for a general Kähler manifold and derive the...

Computing the Level of a Modular Rigid Calabi-Yau Threefold