Ampleness criteria for algebraic spaces
type: Item
instance of: scholarly article
title: Ampleness criteria for algebraic spaces
zbMATH Open document ID: 0553.14004
DOI: 10.1007/BF01275580
author: Pere Pascual-Gainza
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: In this paper are proven three criteria for the ampleness of invertible sheaves over an algebraic space X over a field k: the cohomological criterion, Nakai-Moishezon's and Grauert's. The proof of the Nakai- Moishezon criterion follows the same way as for schemes, and we deduce the cohomological criterion from this one avoiding the use of points and Zariski topology used in EGA III. The proof of Grauert's criterion is based on a gometric interpretation of multiplicity due to Ramanujam.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14A20
Mathematics Subject Classification ID: 14C17
zbMATH DE Number: 3880850
zbMATH Keywords: ampleness of invertible sheaves
zbMATH Keywords: algebraic space
zbMATH Keywords: Nakai-Moishezon criterion
zbMATH Keywords: positive sheaf
zbMATH Keywords: intersection number
MaRDI profile type: Publication
cites work: On the Hilbert-Samuel polynomial in complex analytic geometry
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cites work: Ample subvarieties of algebraic varieties. Notes written in collaboration with C. Musili
cites work: Toward a numerical theory of ampleness
cites work: Algebraic spaces
cites work: On a geometric interpretation of multiplicity
description: scientific article; zbMATH DE number 3880850