Some results on ampleness and divisorial schemes

Mario Borelli
1967 Pacific Journal of Mathematics  
The purpose of this note is twofold. Part I consists of an example of an algebraic scheme which is the union of two closed, quasi-projective subscheme, but which is not itself quasiprojective. The main result of Part II is a structure theorem for coherent sheaves over divisorial schemes and, as an application, the proof that Theorem 2 of Borel-Serre's paper "Le Theorem de Riemann-Roch", which is stated only for quasiprojective, nonsingular schemes, can be extended to arbitrary nonsingular schemes.
doi:10.2140/pjm.1967.23.217 fatcat:tqpiantgvvgkfoiminf2erl4am