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Secant Spaces to Curves

Published online by Cambridge University Press:  20 November 2018

Joachim von Zur Gathen
Joachim von Zur Gathen*
Affiliation:
University of Toronto, Toronto, Ontario
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A classical question in algebraic geometry is whether a given projection of a projective space induces an isomorphism on a given closed subvariety. To answer it, one investigates secant lines to the subvariety. There has been a lot of recent activity in this field ([12], [14],[18], [21], [23]): see [14] and [12] for references).

An obvious generalization of the secant lines is provided by the secant r-planes, which intersect a given closed subvariety in r + 1 linearly independent points. The closure of the set of these secant r-planes is the secant variety, and the aim of this paper is to determine its rational equivalence class in the case of curves. There is an extensive classical literature about this problem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 4 , 01 August 1983 , pp. 589 - 612
Copyright
Copyright © Canadian Mathematical Society 1983

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