  We present the Kormendy and mass-size relations for early-type galaxies
(ETGs) as a function of environment at z~1.3. Our sample includes 76 visually
classified ETGs with masses 10^10 < M/Msun < 10^11.5, selected in the Lynx
supercluster and in the GOODS/CDF-S field, 31 ETGs in clusters, 18 in groups
and 27 in the field, all with multi-wavelength photometry and HST/ACS
observations. The Kormendy relation, in place at z~1.3, does not depend on the
environment. The mass-size relation reveals that ETGs overall appear to be more
compact in denser environments: cluster ETGs have sizes on average around
30-50% smaller than those of the local universe, and a distribution with a
smaller scatter, whereas field ETGs show a mass-size relation with a similar
distribution than the local one. Our results imply that (1) the mass-size
relation in the field did not evolve overall from z ~ 1.3 to present; this is
interesting and in contrast to the trend found at higher masses from previous
works; (2) in denser environments, either ETGs have increased their size by
30-50%, on average, and spread their distributions, or more ETGs have been
formed within the dense environment from not ETG progenitors or larger galaxies
have been accreted to a pristine compact population to reproduce the mass-size
relation observed in the local Universe. Our results are driven by galaxies
with masses M<2*10^11Msun and those with masses M~10^11Msun follow the same
trends that the entire sample. Following Valentinuzzi et al. definition of
superdense ETGs, around 35-45% of our cluster sample is made of superdense
ETGs.
