Mathematics – Algebraic Geometry
Scientific paper
2006-05-29
Mathematics
Algebraic Geometry
LaTeX, 57 pages
Scientific paper
The primitive curves are the multiple curves that can be locally embedded in smooth surfaces (we will always suppose that the associated reduced curves are smooth). These curves have been defined and studied by C. Banica and O.Forster in 1984. In 1995, D. Bayer and D. Eisenbud gave a complete description of the double curves. We give here a parametrization of primitive curves of arbitrary multiplicity. Let Z_n=spec(\C[t]/(t^n)). The curves of multiplicity n are obtained by taking an open cover (U_i) of a smooth curve C and by glueing schemes of type U_i X Z_n using automorphisms of U_{ij} X Z_n that leave U_{ij} invariant. This leads to the study of the sheaf of nonabelian groups G_n of automorphisms of C X Z_n that leave the reduced curve invariant, and to the study of its first cohomology set. We prove also that in most cases it is the same to extend a primitive curve C_n of multiplicity n to one of multiplicity n+1, and to extend the quasi locally free sheaf D_n of derivations of C_n to a rank 2 vector bundle on C_n.
No associations
LandOfFree
Paramétrisation des courbes multiples primitives does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Paramétrisation des courbes multiples primitives, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Paramétrisation des courbes multiples primitives will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-168179