Varieties cut out by quadrics: Scheme-theoretic versus homogeneous generation of ideals

  • Lawrence Ein
  • David Eisenbud
  • Sheldon Katz
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1311)


In this note we consider cases in which a curve in ℙr which is scheme theoretically the intersection of quadrics necessarily has homogeneous ideal generated by quadrics. The first case in which this does not happen is for a general elliptic octic in ℙ5; we give a proof of this using the surjectivity of the period map for K3 surfaces.


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Lawrence Ein
  • David Eisenbud
  • Sheldon Katz

There are no affiliations available

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