Abstract
Here we show that certain low rank ACM vector bundles on scrolls over smooth curves are iterated extensions of line bundles.
Similar content being viewed by others
References
Arrondo, E., Madonna, C.: Curves and vector bundles on quartic threefolds, arXiv:math/0703413
Ballico, E.: ACM vector bundles on products of smooth curves, preprint
Buchweitz, R.-O., Eisenbud, D., Herzog, J.: Cohen-Macaulay modules on quadrics, Singularities, representations of algebras, and vector bundles (Lamprecht, 1985), 58–116, Lecture Notes in Math., 1273, Springer, Berlin, 1987
Buchweitz, R.-O., Greuel, G.-M., Schreyer, F.-O.: Cohen-Macaulaymodules on hyperface singularities. I, Invent. Math., 88 (1987), no. 1, 165–182
Casanellas, M., Drodz, E., Hartshorne, R.: Gorenstein liaison and ACM sheaves, J. Reine Angew. Math., 584 (2005), 149–171
Casanellas, M., Hartshorne, R.: ACM bundles on cubic hypersurfaces, arXiv:math/0801.3600
Chang, M.-C.: Characterization of arithmetically Buchsbaum subschemes of codimension 2 in ℙn, J. Differential Geom., 31 (1990), no. 2, 323–341
Chiantini L., Madonna, C.: ACM bundles on general hypersurfaces in P 5 of low degree, Collect. Math., 56 (2005), no. 1, 85–96
Costa, L., Miró-Roig, R. M.: m-blocks collections and Castelnuovo-Mumford regularity in multiprojective spaces, Nagoya Math. J., 186 (2007), 119–155
Faenzi, D.: Bundles over the Fano threefold V 5, Comm. Algebra, 33 (2005), no. 9, 3061–3080
Faenzi, D.: Bundles over Fano threefolds of type V 22, Ann. Mat. Pura Appl., (4) 186 (2007), no. 1, 1–25
Hoffman, J. W., Wang, H. H.: Castelnuovo-Mumford regularity in biprojective spaces, Adv. Geom., 4 (2004), no. 4, 513–536
Fujita, T.: Cancellation problem of complete varieties, Invent. Math., 64 (1981), no. 1, 119–121
Knörrer, H.: Cohen-Macaulay modules on hypersurface singularities. I, Invent. Math., 88 (1987), no. 1, 153–164
Madonna, C. G.: ACM vector bundles on prime Fano threefolds and complete intersection Calabi Yau threefolds, Rev. Roumaine Math. Pures Appl., 47 (2002), no. 2, 211–222
Okonek, C., Schneider, M., Spindler, H.: Vector bundles on projective spaces, Birkhäuser, Boston, 1980.
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by MIUR and GNSAGA of INDAM (Italy)
Rights and permissions
About this article
Cite this article
Ballico, E. ACM vector bundles on scrolls. Rend. Circ. Mat. Palermo 57, 173–179 (2008). https://doi.org/10.1007/s12215-008-0011-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12215-008-0011-x