| Linear series can be viewed as spaces of sections of line bundles or as projective spaces of linearly equivalent divisors, and thus as special subschemes of fibers of Abel maps. For singular curves of compact type Eisenbud and Harris introduced the notion of limit linear series in the 80's, whereas recently, Abel maps of degree 1 have been constructed for any stable curve by Caporaso and myself, which allowed for the construction and study of Abel maps of any degree for curves of compact type by Coelho and Pacini. In this talk we will see how refined limit linear series or more generally Osserman's exact limit linear series can be associated to certain subschemes of fibers of Abel maps in the simplest case of a two-component curve of compact type. This is joint work with Brian Osserman (Davis University). |