On the moduli scheme of stable sheaves supported on cubic space curves

2002/04/30 by Hans-Georg Freiermuth, Guenther Trautmann · 1 citation
Mathematics · #math.AG #msc:14F05 #msc:18F20 #msc:14D20 #msc:14D22

paper · pdf

published as Amer. J. Math. 126, 2 (2004), 363-393 · 28 pages, LaTeX; minor changes, to appear in Amer. J. Math

arxiv created 2003/03/08 · arxiv updated 2009/11/30

Abstract

We investigate the geometry of the Simpson moduli space M of stable sheaves on P₃ with Hilbert polynomial H(m)=3m+1 and describe explicitly the two smooth, rational components, their 11-dimensional smooth, transversal intersection and the relation between M and the Hilbert scheme Hilb_H(P₃) of cubic space curves. We also compute the Betti numbers of the Chow groups of the moduli space M.

Cited by

• Quintic genus 2 curves, stable pairs and wall-crossing

Related

• Moduli of stable sheaves supported on curves of genus three contained in a quadric surface
• The geometry of the moduli space of one-dimensional sheaves
• Moduli of sheaves supported on quartic space curves
• Hilbert scheme of rational cubic curves via stable maps
• Moduli of sheaves supported on curves of genus two in a quadric surface