Calabi-Yau manifolds are compact Kähler manifolds
whose canonical bundle is trivial.
In superstring theory the extra dimensions of spacetime
may take the form of a 6-dimensional Calabi–Yau manifold.
"Canonical bundle" is just another name for "invertible sheaf."
An invertible sheaf is exactly like a line bundle, only
transposed from topology into algebraic geometry.
Real line bundles are double covers of differential manifolds,
and now we arrive at a relatively familiar example:
A Mobius strip is a double cover of a circle!
