Full paper in PDF:
$% E. Ballico, R. Notari, and M. L. Spreafico, Ropes on a line embedded in a Grassmannian variety, Rev. Mat. Complut. 17 (2004), 181–193.%$

Ropes on a Line Embedded in a Grassmannian Variety

Edoardo BALLICO, Roberto NOTARI,
and Maria Luisa SPREAFICO
Dipartimento di Matematica,

Università di Trento,
I-38050 Povo (Tn) — Italy
ballico@science.unitn.it

Dipartimento di Matematica,

Politecnico di Torino,
I-10129 Torino — Italy
roberto.notari@polito.it
Dipartimento di Matematica,
Politecnico di Torino,
I-10129 Torino — Italy
maria.spreafico@polito.it

Received: October 21, 2002
Accepted: October 13, 2003
ABSTRACT

Let L be a line contained in a Grassmannian variety G. A d-rope C < G supported on L is a locally Cohen-Macaulay curve of degree d with Cred = L and (IL,G)2 <I C,G. We characterize the d-ropes C supported on L and embedded in G. In some cases we describe also the vector bundles on such a rope C. Finally, we describe the parameter spaces for ropes embedded in G.

Key words: multiple line, Grassmannian variety, normal sheaf, embeddings.
2000 Mathematics Subject Classification: Primary 14C05, 14M15; Secondary 14H99.