Abstract: Reider's Theorem on very ampleness of divisors of the form \(K_S + D\) on a non-singular surface has a natural generalization to ampleness of divisors of the form \((K_S + D)_d - \Delta\) on the Hilbert schemes of d points on \(S\). The boundary case, where we can prove the divisor is nef but not ample, is a very natural generalization of the pull-back of \(2\Theta\) under the Abel-Jacobi map for curves. In light of Mumford's theorem for surfaces with \(p_g\) different from zero, these nef divisors surprised us. In this talk I will explain some interesting geometry for particular surfaces and also sketch the proof, which relies on results of Bayer-Macrì and Toda on Bridgeland stability conditions on surfaces.