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This article wants to show two things: first, that certain problems inDiophantus' Arithmetica lead to equations defining del Pezzo surfaces or otherrational surfaces, while certain others lead to K3 surfaces; second, thatDiophantus' own solutions to these problems, when viewed through a modern lens,lead to parametrizations of these surfaces, or of parametrizations of rationalcurves lying on them.

Diophantus Revisited: On rational surfaces and K3 surfaces in the Arithmetica