Restricting linear syzygies : algebra and geometry

  title={Restricting linear syzygies : algebra and geometry},
  author={David Eisenbud and Mark Green and K. Hulek and Stefan Popescu},
Let X ⊂ Pr be a closed scheme in projective space whose homogeneous ideal is generated by quadrics. We say that X (or its ideal IX) satisfies the condition N2,p if the syzygies of IX are linear for p steps. We show that if X satisfies N2,p then a zero-dimensional or one-dimensional intersection of X with a plane of dimension p is 2-regular. This extends a result of Green and Lazarsfeld. We give conditions when the syzygies of X restrict to the syzygies of the intersection. Many of our results… CONTINUE READING
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