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

Comment: 27 pages, final version

• 14B05 - Singularities in algebraic geometry
• 14G17 - Positive characteristic ground fields in algebraic geometry
• 14J17 - Singularities of surfaces or higher-dimensional varieties
• 14J26 - Rational and ruled surfaces

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