Holomorphic Yukawa couplings for complete intersection Calabi-Yau manifolds

Holomorphic parabolic geometries and Calabi-Yau manifolds

We prove that the only complex parabolic geometries on Calabi–Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.

Generalized Calabi-Yau manifolds

A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2-forms. In the special case of six dimensions we characterize them as critical points of a natural variational problem on clos...

Calabi–Yau manifolds for dummies

In the text below we try to introduce the concept of a Calabi–Yau manifold. We start by defining vector bundles and complex manifolds, then introduce Kähler manifolds, review the most rudimentary concepts of Chern classes and then define Calabi–Yau manifolds. We also comment on the importance of Calabi–Yau manifolds in physics. As an example to guide us on the way, we have chosen the two-sphere...

Calabi-Yau Manifolds

Rigid curves in complete intersection Calabi-Yau threefolds

Working over the complex numbers, we study curves lying in a complete intersection K3 surface contained in a (nodal) complete intersection Calabi-Yau threefold. Under certain generality assumptions, we show that the linear system of curves in the surface is a connected componend of the the Hilbert scheme of the threefold. In the case of genus one, we deduce the existence of infinitesimally rigi...