Morfismos de Abel, series lineales y sus límites sobre curvas

RESUMEN. We introduce the main results and techniques related to the constructions of the moduli spaces of linear series, limit linear series on curves and its relations with Abel maps. We start with a brief exposition of the theory of the linear series and its main consequences on smooth curves. Also, we examine two constructions of limits of linear series and their moduli spaces: Eisenbud and Harris types [14] and Osserman types [42]. In addition, we discuss the relation of the latter construction with Abel maps [22] and we present a new limits construction: Esteves-Nigro-Rizzo types [20,21] which generalize Eisenbud-Harris and Osserman constructions. Finally, we give a brief overview on further works related to these theories and their applications.