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.
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