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We proved the convergence of a sequence of 2 dimensional comapctKahler-Einstein orbifolds with rational quotient singularities and with someuniform bounds on the volumes and on the Euler characteristics of our orbifodsto a Kahler-Einstein 2-dimensional orbifold. Our limit orbifold can have worsesingularities than the orbifolds in our sequence. We will also derive someestimates on the norms of the sections of plurianticanonical bundles of ourorbifolds in the sequence that we are considering and our limit orbifold.

Convergence of Kähler-Einstein orbifolds