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In this note we consider a singular Liouville equation on compact surfaces, arising from the study of Chern-Simons vortices. Using improved versions of the Moser-Trudinger inequality and a min-max scheme, we prove existence of solutions in cases with lack of coercivity. Full details and further references can be found in the forthcoming paper  .doi:10.4171/rlm/577 fatcat:2avdj3vojrb27ci5w3zcmjlldu