Non-classical trigonal curves

We study trigonal Gorenstein curves of arithmetic genus g ≥ 5 such that g⅓ has a base point, through realizing them as canonical curves lying over a cone. Using an explicit description of such curves we compute the dimension of their moduli spaces. We also investigate non-classical trigonal Gorenstein curves; in fact, we give a complete classification of such curves for arithmetic genus g = 5. More generally, we classify the non-classical curves when the characteristic of the constant field is g - 1, g - 2, or 2g - 3. In characteristic 2 we also solve the case g = 2n + 1.