The first stages of the evolution of Globular Clusters
  The majority of the inhomogeneities in the chemical composition of Globular Cluster (GC) stars appear due to primordial enrichment. The most studied model today claims that the ejecta of Asymptotic Giant Branch (AGB) stars of high mass -those evolving during the first ~100Myr of the Clusters life- directly form a second generation of stars with abundance anomalies. In this talk, we review the status of the art with regard to this model, whose major problems are i) the modelling of the chemical anomalies is still not fully complete, and ii) it requires an IMF peculiarly enhanced in the intermediate mass stars. The model predicts enhanced helium abundance in the stars showing chemical anomalies, and the helium abundance distribution can be roughly derived from the morphology of the horizontal branch. Such distribution may possibly help to falsify the model for the first phases of evolution of GCs. As an illustration, we compare the results of the analysis of the HB morphology of some clusters. 
Francesca D'Antona, Paolo Ventura and Vittoria Caloi