Diophantine approximations and toric deformations
1.1. Let S be a finite set of places of a finite field extension L of a number field K, containing all infinite places. Let E be a vector space over K of dimension N + 1. For v ∈ S, let lv0, · · · , lvN be linearly independent vectors in E ⊗K L. Choose a projective subvariety X defined over K, embedded into the projective space P(E∨) of lines of the dual vector space E∨. Consider the system of inequalities