SOME EXAMPLES OF CALABI-YAU 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

Convergence of Calabi-Yau manifolds

In this paper, we study the convergence of Calabi-Yau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi-Yau manifolds.

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...

Non-Commutative Calabi-Yau Manifolds

We discuss aspects of the algebraic geometry of compact non-commutative CalabiYau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi-Yau algebra. We consider two examples: a toroidal orbifold T /Z2×Z2, and an orbifold of the quintic in CP4, each with discrete torsion. The non-commutative geometry tools are enoug...