Some Basic Constructions in the Category of Projective k-Varieties

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

Chapter Chapter 21 in A Royal Road to Algebraic Geometry, 2012, pp 335-341 from Springer

Abstract: Abstract In this chapter we assume, basically for simplicity only, that all schemes be projective varieties over a field (of any characteristic unless otherwise stated), which without significant loss of generality may be assumed algebraically closed. The chapter gives some basic constructions in the category of projective k-varieties: the blowing-up of a closed subscheme and of subbundles. We introduce the Grassmann bundles, and the related construction of a parameter variety for the joining lines for a projective, embedded scheme. The secant variety and the join are given as applications of these constructions.

Keywords: Basic Construction; Grassmann Bundle; Secant Variety; Embedding Scheme; Line Joining (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_21

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DOI: 10.1007/978-3-642-19225-8_21

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