Complutense University Library

Cohomological characterization of vector bundles on Grassmannians of lines


Arrondo Esteban, Enrique and Malaspina, Francesco (2010) Cohomological characterization of vector bundles on Grassmannians of lines. Journal of Algebra, 323 (4). pp. 1098-1106. ISSN 0021-8693

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:


We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give. in the line of previous results by Costa and Miro-Roig, a cohomological characterization of exterior and symmetric powers of the universal bundles of the Grassmannian.

Item Type:Article
Uncontrolled Keywords:Castelnuovo-Mumford regularity; Criterion; Quadrics; Spaces
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14754

[1] E. Arrondo, B. Graña, Vector bundles on G(1, 4) without intermediate cohomology, J. Algebra 214 (1999) 128–142.

[2] E. Ballico, F. Malaspina, Qregularity and an extension of the Evans–Griffiths criterion to vector bundles on quadrics, J. Pure

Appl. Algebra 213 (2009) 194–202.

[3] J.V. Chipalkatti, A generalization of Castelnuovo regularity to Grassmann varieties, Manuscripta Math. 102 (4) (2000) 447–


[4] L. Costa, R.M. Miró-Roig, Cohomological characterization of vector bundles on multiprojective spaces, J. Algebra 294 (1)

(2005) 73–96, with a corrigendum in: J. Algebra 319 (3) (2008) 1336–1338.

[5] L. Costa, R.M. Miró-Roig, m-blocks collections and Castelnuovo–Mumford regularity in multiprojective spaces, Nagoya

Math. J. 186 (2007) 119–155.

[6] E.G. Evans, P. Griffith, The syzygy problem, Ann. of Math. 114 (2) (1981) 323–333.

[7] J.W. Hoffman, H.H. Wang, Castelnuovo–Mumford regularity in biprojective spaces, Adv. Geom. 4 (4) (2004) 513–536.

[8] H. Knörrer, Cohen–Macaulay modules on hypersurface singularities I, Invent. Math. 88 (1987) 153–164.

[9] F. Malaspina, Few splitting criteria for vector bundles, Ric. Mat. 57 (2008) 55–64.

[10] D. Mumford, Lectures on Curves on an Algebraic Surface, Princeton University Press, Princeton, NJ, 1966.

[11] G. Ottaviani, Some extension of Horrocks criterion to vector bundles on Grassmannians and quadrics, Ann. Mat. Pura Appl.

(IV) 155 (1989) 317–341.

Deposited On:17 Apr 2012 11:32
Last Modified:06 Feb 2014 10:08

Repository Staff Only: item control page