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We determine all configurations of rational double points that occur on RDPdel Pezzo surfaces of arbitrary degree and Picard rank over an algebraicallyclosed field $k$ of arbitrary characteristic ${\rm char}(k)=p \geq 0$,generalizing classical work of Du Val to positive characteristic. Moreover, wegive simplified equations for all RDP del Pezzo surfaces of degree $1$containing non-taut rational double points.

Which rational double points occur on del Pezzo surfaces?