A Generic Cubic Surface Contains No Involutive Curve

In 1988, J. Bernstein and V. Lunts (Invent. Math.94, 223–243) proved that a generic surface in 3 of degree 4 or greater would not contain a curve which supported a module over the second Weyl algebra. It is known that quadric surfaces and planes always do. This paper shows that a generic cubic surface does not.