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Is there an elegant way to find the singularities of an algebraic variety

  1. Dec 3, 2007 #1

    frb

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    Let V be the variety of the ideal (f)

    a singular point is a point where all the partial derivatives of the f are zero.
    I know you can find singular points by writing down all these partial derivatives and also that the points are zeros of f (such as all points on the variety) and solve that system of equations. These are generally very difficult systems to solve so I wondered if there was a more elegant method to find these singular points.
     
    Last edited: Dec 3, 2007
  2. jcsd
  3. Dec 3, 2007 #2

    Chris Hillman

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    Have you read Cox, Little, O'Shea, Ideals, Varieties and Algorithms? One of the best books ever published.
     
  4. Dec 3, 2007 #3

    frb

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    No, but I was trying to avoid resorting to mere number crunching. Seems like there is no other way...
     
  5. Dec 3, 2007 #4

    Chris Hillman

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    I was thinking of computational algebra as in "symbolic computation", not numerical computation. Groebner bases are a student's best friend!
     
  6. Dec 3, 2007 #5

    mathwonk

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    if by "find" you mean compute, why does "number crunching" seem inappropriate?
     
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