The feasibility for a measurement of the exclusive production of a real photon, a process although known as Deeply Virtual Compton Scattering (DVCS) at an Electron Ion Collider (EIC) has been explored. DVCS is universally believed to be a golden measurement toward the determination of the Generalized Parton Distribution (GPDs) functions. The high luminosity of the machine, expected in the order of 10^34 cm^-2 s^-1 at the highest center-of-mass energy, together with the large resolution and rapidity acceptance of a newly designed dedicated detector, will open a opportunity for very high precision measurements of DVCS, and thus for the determination of GPDs, providing an important tool toward a 2+1 dimensional picture of the internal structure of the proton and nuclei.
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