Application of a Numerical Version of Terr Acini’s Lemma for Secants and Joins

  • Daniel J. Bates
  • Chris Peterson
  • Andrew J. Sommese
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 146)


This paper illustrates how methods such as homotopy continuation and monodromy, when combined with a numerical version of Terracini’s lemma, can be used to produce a high probability algorithm for computing the dimensions of secant and join varieties. The use of numerical methods allows applications to problems that are difficult to handle by purely symbolic algorithms.

Key words

Generic point witness point homotopy continuation irreducible components numerical algebraic geometry monodromy polynomial system secant join 

AMS(MOS) subject classifications

Primary 65H10 65H20 68W30 14Q99 14M99 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Daniel J. Bates
    • 1
  • Chris Peterson
    • 2
  • Andrew J. Sommese
    • 3
  1. 1.Institute for Mathematics and Its Applications (IMA)University of MinnesotaMinneapolis
  2. 2.Department of MathematicsColorado State UniversityFort Collins
  3. 3.Department of MathematicsUniversity of Notre DameNotre Dame

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