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

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