Vol. 23, No. 2, 1967

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Some results on ampleness and divisorial schemes

Mario Borelli

Vol. 23 (1967), No. 2, 217–227

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 Théorèm de Riemann-Roch”, which is stated only for quasiprojective, nonsingular schemes, can be extended to arbitrary nonsingular schemes. (See the Remark on page 108 of the mentioned paper.)

Mathematical Subject Classification
Primary: 14.55
Received: 29 August 1966
Published: 1 November 1967
Mario Borelli