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Rational curves of Castelnuovo–Mumford regularity [formula omitted]

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
321
Issue
9
Identifiers
DOI: 10.1016/j.jalgebra.2009.01.015
Keywords
  • Castelnuovo–Mumford Regularity
  • Defining Equation
  • Rational Curve
  • Secant Line

Abstract

Abstract The purpose here is to show that for r ⩾ 4 and d ⩾ r + 4 , a nondegenerate rational curve of degree d in P r has a unique ( d − r + 1 ) -secant line if and only if X fails to be ( d − r ) -regular. This is a next case to a result of Gruson, Lazarsfeld and Peskine, which asserts that for r ⩾ 3 and d ⩾ r + 2 , a nondegenerate curve X of degree d in P r has a ( d − r + 2 ) -secant line if and only if X fails to be ( d − r + 1 ) -regular.

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