  We investigate the deformations of pairs $(X,L)$, where $L$ is a line bundle
on a smooth projective variety $X$, defined over an algebraically closed field
$\mathbb{K}$ of characteristic 0. In particular, we prove that the DG-Lie
algebra controlling the deformations of the pair $(X,L)$ is homotopy abelian
whenever $X$ has trivial canonical bundle, and so these deformations are
unobstructed.
