A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold -- which is viewed as the obstruction to the existence of a Q-invariant Berezin volume -- is not well know. We review the basic ideas and then apply this technology to various examples, including $L_{ \infty}$-algebroids and higher Poisson manifolds.
Categories: math.DG math-ph math.MP math.QA math.SG