Betti numbers of space curves bounded by Hilbert functions

  • Renato Maggioni
  • Alfio Ragusa
Keywords: Dubreil's theorem, Betti numbers, Hilbert function, Bilinked curves


We study relationships between Hilbert functions and graded Betti numbers of two space curves C and C_0 bilinked by a sequence of basic double linkages; precisely we obtain bounds for the graded Betti numbers of C by means of the Hilbert functions of the two curves and the graded Betti numbers of C_0 . On the other hand for every set of integers satisfying these bounds we can construct a curve with these integers as its graded Betti numbers. As a consequence we get a Dubreil-type theorem for a curve C which strongly dominates C_0 at height h which is exactly the Amasaki bound for Buchsbaum curves. Moreover we deduce for biliaison classes of Buchsbaum curves that a strong Lazarsfeld-Rao property holds.