Families of space curves with large cohomology

Nadia Chiarli, Silvio Greco, Uwe Nagel

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We investigate space curves with large cohomology. To this end we introduce curves of subextremal type. This class includes all subextremal curves. Based on geometric and numerical characterizations of curves of subextremal type, we show that, if the cohomology is "not too small," then they can be parameterized by the union of two generically smooth irreducible families; one of them corresponds to the subextremal curves. For curves of negative genus, the general curve of each of these families is also a smooth point of the support of an irreducible component of the Hilbert scheme. The two components have the same (large) dimension and meet in a subscheme of codimension one.

Original languageEnglish
Pages (from-to)704-726
Number of pages23
JournalJournal of Algebra
Issue number2
StatePublished - Jan 15 2007


  • Hartshorne-Rao module
  • Hilbert scheme
  • Space curves
  • Subextremal type

ASJC Scopus subject areas

  • Algebra and Number Theory


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