In recent years, the disk populations in a number of young star-forming regions have been surveyed with ALMA. Understanding the disk properties and their correlation with those of the central star is critical to understand planet formation. In particular, a decrease of the average measured disk dust mass with the age of the region has been observed. We conducted high-sensitivity continuum ALMA observations of 43 Class II young stellar objects in CrA at 1.3 mm (230 GHz). The typical spatial resolution is 0.3. The continuum fluxes are used to estimate the dust masses of the disks, and a survival analysis is performed to estimate the average dust mass. We also obtained new VLT/X-Shooter spectra for 12 of the objects in our sample. 24 disks are detected, and stringent limits have been put on the average dust mass of the non-detections. Accounting for the upper limits, the average disk mass in CrA is $6pm3,rm M_oplus$, significantly lower than that of disks in other young (1-3 Myr) star forming regions (e.g. Lupus) and appears consistent with the 5-10 Myr old Upper Sco. The position of the stars in our sample on the HR diagram, however, seems to confirm that that CrA has age similar to Lupus. Neither external photoevaporation nor a lower than usual stellar mass distribution can explain the low disk masses. On the other hand, a low-mass disk population could be explained if the disks are small, which could happen if the parent cloud has a low temperature or intrinsic angular momentum, or if the the angular momentum of the cloud is removed by some physical mechanism such as magnetic braking. In order to fully explain and understand the dust mass distribution of protoplanetary disks and their evolution, it may also be necessary to take into consideration the initial conditions of star and disk formation process, which may vary from region to region, and affect planet formation.
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