Cayley deformations of compact complex surfaces

In this article, we consider Cayley deformations of a compact complex surface in a Calabi–Yau fourfold. We will study complex deformations of compact complex submanifolds of Calabi–Yau manifolds with a view to explaining why complex and Cayley deformations of a compact complex surface are the same

Deformations of Conically Singular Cayley Submanifolds

In this article, we study the deformation theory of conically singular Cayley submanifolds. In particular, we prove a result on the expected dimension of a moduli space of Cayley deformations of a conically singular Cayley submanifold. Moreover, when the Cayley submanifold is a two-dimensional complex submanifold of a Calabi–Yau four-fold, we show by comparing Cayley and complex deformations that in this special case the moduli space is a smooth manifold. We also perform calculations of some of the quantities discussed for some examples