Title: The Minimal Resolution Conjecture on a general quartic surface in $\mathbb P^3$,
Abstract: Mustaţă has given a conjecture for the graded Betti numbers in the
minimal free resolution of the ideal of a general set of points on an
irreducible projective algebraic variety. For surfaces in $\mathbb P^3$ this
conjecture has been proven for points on quadric surfaces and on general cubic
surfaces. In the latter case, Gorenstein liaison was the main tool. Here we
prove the conjecture for general quartic surfaces. Gorenstein liaison continues
to be a central tool, but to prove the existence of our links we make use of
certain dimension computations. We also discuss the higher degree case, but now
the dimension count does not force the existence of our links.