Abel Maps and Presentation Schemes

Details Abel Maps and Presentation Schemes Abel Maps and Presentation Schemes

1999-11-10

arxiv.org/abs/math/9911069v2

Mathematics

Algebraic Geometry

Plain TeX, 32 pages. This is the final version, to appear in the Hartshorne issue of the Communications in Algebra. A number o

Scientific paper

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 smoothness theorem for bigraded Abel maps. Second we study the two complementary filtrations provided by the images of certain Abel maps and certain presentation 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 is a IP^1-bundle. Finally, using Abel maps of bidegree (m,1), we characterize the curves having double points at worst

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