The Hilbert scheme of degree two curves and certain ropes

Uwe Nagel, Roberto Notari, Maria Luisa Spreafico

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study families of ropes of any codimension that are supported on lines. We construct suitable smooth parameter spaces and conclude that all ropes of fixed degree and genus lie in the same component of the corresponding Hilbert scheme. We show that this component is generically smooth if the genus is small enough unless the characteristic of the ground field is two and the curves under consideration have degree two. In this case the component is non-reduced.

Original languageEnglish
Pages (from-to)835-867
Number of pages33
JournalInternational Journal of Mathematics
Issue number7
StatePublished - Aug 2006

Bibliographical note

Funding Information:
The authors warmly thank INDAM-GNSAGA for partial support. The first author was also partially supported by a Faculty Summer Research Fellowship from the University of Kentucky.


  • Curves
  • Hilbert scheme
  • Minimal free resolution
  • Normal sheaf
  • Ropes

ASJC Scopus subject areas

  • General Mathematics


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