  We present an approach to Green-Lazarsfeld's generic vanishing combining
gaussian maps and the Fourier-Mukai transform associated to the Poincar\`e line
bundle. As an application we prove the Generic Vanishing Theorem for all normal
Cohen-Macaulay subvarieties of abelian varieties over an algebraically closed
field. This paper is a reworking of part of arXiv:math/0310026v2 [math.AG],
which contained a mistake.
