  Let $(A,\Theta)$ be a principally polarised abelian variety, and let Y be a
subvariety. Pareschi and Popa conjectured that Y has minimal cohomology class
if and only if the structure sheaf of Y satisfies a property that they call
M-regularity.
  Let now X be a smooth cubic threefold. By a classical result due to Clemens
and Griffiths, its intermediate Jacobian J(X) is a principally polarised
abelian variety; furthermore the Fano surface of lines on X can be embedded in
J(X) and has minimal cohomology class. In this short note we show that its
structure sheaf is M-regular.
