Divisors on Mg,g+1 and the Minimal Resolution Conjecture for points on canonical curves

We use geometrically defined divisors on moduli spaces of pointed curves to compute the graded Betti numbers of general sets of points on any nonhyperelliptic canonically embedded curve. This gives a positive answer to the Minimal Resolution Conjecture in the case of canonical curves. But we prove that the conjecture fails on curves of large degree. These results are related to the existence of theta divisors associated to certain stable vector bundles. (C) 2003 Editions scientifiques et medicales Elsevier SAS.