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Projective Schemes and Bundles

In: A Royal Road to Algebraic Geometry

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  • Audun Holme

    (University of Bergen, Department of Mathematics)

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.

Suggested Citation

  • Audun Holme, 2012. "Projective Schemes and Bundles," Springer Books, in: A Royal Road to Algebraic Geometry, chapter 0, pages 253-261, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-19225-8_14
    DOI: 10.1007/978-3-642-19225-8_14
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