Tight closure/Graded/Dimension 2/Gorenstein/Finite field/Test ideal exponent/Fact

Let ${}R$ be a standard-graded, two-dimensional (geometrically) normal Gorenstein domain over a finite field. Fix ${}n$ and suppose that ${}p=4(g-1)(n-1)^{3}$, where ${}g$ is the genus of the curve.

Then there exists a test ideal exponent for the class of primary homogeneous ideals generated by ${}n$ elements.

Write a proof