Is the Picard group computable by a computer algebra system?

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My question is, as the title suggests:



Given the defining ideal of a variety $X$ (over $mathbb C$), can we compute $Pic(X)$ with a computer algebra system?



Even if the answer is no in general, are there conditions under which this is possible (e.g. $X$ a curve, a K3-surface, smooth,...)?




algebraic-geometry computability computational-geometry computer-algebra-systems picard-scheme




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    up vote
    1
    down vote

    favorite












    My question is, as the title suggests:



    Given the defining ideal of a variety $X$ (over $mathbb C$), can we compute $Pic(X)$ with a computer algebra system?



    Even if the answer is no in general, are there conditions under which this is possible (e.g. $X$ a curve, a K3-surface, smooth,...)?




    algebraic-geometry computability computational-geometry computer-algebra-systems picard-scheme




    share|cite|improve this question





















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      My question is, as the title suggests:



      Given the defining ideal of a variety $X$ (over $mathbb C$), can we compute $Pic(X)$ with a computer algebra system?



      Even if the answer is no in general, are there conditions under which this is possible (e.g. $X$ a curve, a K3-surface, smooth,...)?




      algebraic-geometry computability computational-geometry computer-algebra-systems picard-scheme




      share|cite|improve this question











      My question is, as the title suggests:



      Given the defining ideal of a variety $X$ (over $mathbb C$), can we compute $Pic(X)$ with a computer algebra system?



      Even if the answer is no in general, are there conditions under which this is possible (e.g. $X$ a curve, a K3-surface, smooth,...)?





      algebraic-geometry computability computational-geometry computer-algebra-systems picard-scheme





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 18 at 12:31









      James

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