Multiple stellar populations in Asymptotic Giant Branch stars of
  Galactic Globular Clusters
  Multiple stellar populations (MPs) are a distinct characteristic of Globular
Clusters (GCs). Their general properties have been widely studied among main
sequence, red giant branch (RGB) and horizontal branch (HB) stars, but a common
framework is still missing at later evolutionary stages. We studied the MP
phenomenon along the AGB sequences in 58 GCs, observed with the Hubble Space
Telescope in ultraviolet (UV) and optical filters. By using UV-optical
color-magnitude diagrams, we selected the AGB members of each cluster and
identified the AGB candidates of the metal-enhanced population in type II GCs.
We studied the photometric properties of AGB stars and compared them to
theoretical models derived from synthetic spectra analysis. We observe the
following features: i) the spread of AGB stars in photometric indices sensitive
to variations of light-elements and helium is typically larger than that
expected from photometric errors; ii) the fraction of metal-enhanced stars in
the AGB is lower than in the RGB in most of the type II GCs; iii) the fraction
of 1G stars derived from the chromosome map of AGB stars in 15 GCs is larger
than that of RGB stars; v) the AGB/HB frequency correlates with the average
mass of the most helium-enriched population. These findings represent a clear
evidence of the presence of MPs along the AGB of Galactic GCs and indicate that
a significant fraction of helium-enriched stars, which have lower mass in the
HB, does not evolve to the AGB phase, leaving the HB sequence towards higher
effective temperatures, as predicted by the AGB-manqu\'e scenario.
