Projective Schemes and Bundles

Audun Holme ()
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Audun Holme: University of Bergen, Department of Mathematics

Chapter Chapter 14 in A Royal Road to Algebraic Geometry, 2012, pp 253-261 from Springer

Abstract: Abstract The chapter starts by defining Proj(S) for a graded ring k[X 0,…,X N ], the scheme-theoretic version of projective N-space. We then immediately move on to Proj (S) for a graded A-algebra S. It is first defined as a Spec(A)-scheme when A is a commutative ring, then we proceed to extended the definition to the important global case of a graded -algebra on a scheme X. Likewise the module corresponding to a graded S-module is defined, as well as the global counterpart for a graded -module on a scheme X.

Keywords: Scheme-theoretic Version; Graded Ring; Commutative Ring; Homogeneous Prime Ideals; Quasi-coherent Sheaves (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-19225-8_14

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DOI: 10.1007/978-3-642-19225-8_14

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