Let L be a line contained in a Grassmannian variety G. A d-rope C ⊂ G sup- ported on L is a locally Cohen-Macaulay curve of degree d with Cred = L and (IL,G)2 ⊂ IC,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.
Ropes supported on a line embedded in a Grassmannian variety / B. E., R. Notari, M.L. Spreafico. - In: REVISTA MATEMATICA COMPLUTENSE. - ISSN 1139-1138. - 17:1(2004), pp. 181-193. [10.5209/rev_REMA.2004.v17.n1.16799]
Ropes supported on a line embedded in a Grassmannian variety
M.L. Spreafico
2004
Abstract
Let L be a line contained in a Grassmannian variety G. A d-rope C ⊂ G sup- ported on L is a locally Cohen-Macaulay curve of degree d with Cred = L and (IL,G)2 ⊂ IC,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.
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