| In this talk I will show some results that have to study the geometry of \(K3\) surfaces with finite automorphism group. In particular, given a family of complex projective \(K3\) surfaces with finite automorphism group and Picard number greater than \(3\), if one knows how to compute its effective cone, i.e. one identifies all the \((−2)\)-curves on the surface, and its nef cone (the dual of its effective cone), and one also knows the theory of linear systems of \(K3\) surfaces (for example the work of Saint-Donat), one can find its projective model (for example the recent work of Xavier Roulleau). |
