Period-Age-Metallicity and Period-Age-Color-Metallicity relations for
  Classical Cepheids: an application to the Gaia EDR3 sample
  Based on updated pulsation models for Classical Cepheids, computed for
various assumptions about the metallicity and helium abundance, roughly
representative of pulsators in the Small Magellanic Cloud ($Z$=$0.004$ and
$Y$=$0.25$), Large Magellanic Cloud ($Z$=$0.008$ and $Y$=$0.25$), and M31
($Z$=$0.03$ and $Y$=$0.28$), and self-consistent updated evolutionary
predictions, we derived Period-Age and multi-band Period-Age-Color relations
that also take into account variations in the Mass-Luminosity relation. These
results, combined with those previously derived for Galactic Cepheids, were
used to investigate the metallicity effect when using these variables as age
indicators. In particular, we found that a variation in the metal abundance
affects both the slope and the zero point of the above-mentioned relations. The
new relations were applied to a sample of Gaia Early Data Release 3 Classical
Cepheids. The retrieved distribution of the individual ages confirms that a
brighter Mass-Luminosity relation produces older ages and that First Overtone
pulsators are found to be concentrated towards older ages with respect to the
Fundamental ones at a fixed Mass-Luminosity relation. Moreover, the inclusion
of a metallicity term in the Period-Age and Period-Age-Color relations slightly
modifies the predicted ages. In particular, the age distribution of the
selected sample of Galactic Cepheids is found to be shifted towards slightly
older values, when the F-mode canonical relations are considered, with respect
to the case at a fixed solar chemical composition. A marginally opposite
dependence can be found in the noncanonical F-mode and canonical FO-mode cases.
