(1.8) A Calabi-Yau variety over $K$ is a smooth, proper, geometrically connected $K$-scheme $X$ such that the canonical line bundle $\omega_{X}$ is trivial. In particular, our definition also includes abelian varieties. A volume form on a Calabi-Yau variety $X$ is a nowhere vanishing differential form of maximal degree, that is, a global generator for the canonical line bundle $\omega_{X}$.