Seidel’s long exact sequence on 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

String Theory on Calabi-yau Manifolds

These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of string theory which occur even at the classical level as well as those which require non-perturbative effects. These lecture notes are based on an evolving set ...

On stability manifolds of Calabi-Yau surfaces

We prove some general statements on stability conditions of CalabiYau surfaces and discuss the stability manifold of the cotangent bundle of P. Our primary interest is in spherical objects.

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.