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  • Gröbner Flags and Gorenstein Algebras

  • Aldo Conca, Maria Evelina Rossi, Giuseppe Valla
  • Journal:
    Compositio Mathematica / Volume 129 / Issue 1 / October 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 95-121
    Print publication:
    October 2001
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  • The goal of this paper is to study the Koszul property and the property of having a Gröbner basis of quadrics for classical varieties and algebras as canonical curves, finite sets of points and Artinian Gorenstein algebras with socle in low degree. Our approach is based on the notion of Gröbner flags and Koszul filtrations. The main results are the existence of a Gröbner basis of quadrics for the ideal of the canonical curve whenever it is defined by quadrics, the existence of a Gröbner basis of quadrics for the defining ideal of s [les ] 2n points in general linear position in Pn, and the Koszul property of the ‘generic’ Artinian Gorenstein algebra of socle degree 3.