It is well-known that the construction of Zariski spectra (commutative) rings yields a dual adjunction between category and locally ringed spaces. There are many constructions algebras in various contexts giving such adjunctions. Michel Coste unified them language categorical logic by showing that, for an appropriate triple $ (T_0,T,\Lambda) (which we call spatial context), each T_0 $-model can...

We investigate effectiveness and ampleness of adjoint divisors the form aL + bKX, where L is a suitably positive line bundle on smooth projective variety X a, b are integers.