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1 results

  • Hilbert Functions and Generic Forms

  • JÜRGEN HERZOG, DORIN POPESCU
  • Journal:
    Compositio Mathematica / Volume 113 / Issue 1 / August 1998
    Published online by Cambridge University Press:
    04 December 2007, pp. 1-22
    Print publication:
    August 1998
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  • Let A be a homogeneous K-algebra where K is a field of characteristic 0, and h ∈ A a generic form. We bound the Hilbert function H(A/(h),-) in terms of H(A,-) which extends the bound given by M. Green for generic linear forms. We apply this to some conjectures from Higher Castelnuovo Theory and Cayley-Bacharach Theory.