Abel maps and presentation schemes

We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smooth ness theorem for bigraded Abel maps. Second we study the two complementary filtrations provided by the images of certain Abel maps and certain present ation schemes. Third we study a lifting of the Abel map of bidegree (m, 1) to the corresponding presentation scheme. Fourth we prove that, if a curve is blown up at a double point, then the corresponding presentation scheme i s a P-1-bundle. Finally, wing Abel maps of bidegree (m, 1), we characterize the curves having double points at worst.