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
Restricted to Repository staff only until 2020.
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.
|Uncontrolled Keywords:||Castelnuovo-Mumford regularity; Criterion; Quadrics; Spaces|
|Subjects:||Sciences > Mathematics > Algebraic geometry|
 E. Arrondo, B. Graña, Vector bundles on G(1, 4) without intermediate cohomology, J. Algebra 214 (1999) 128–142.
 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.
 J.V. Chipalkatti, A generalization of Castelnuovo regularity to Grassmann varieties, Manuscripta Math. 102 (4) (2000) 447–
 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.
 L. Costa, R.M. Miró-Roig, m-blocks collections and Castelnuovo–Mumford regularity in multiprojective spaces, Nagoya
Math. J. 186 (2007) 119–155.
 E.G. Evans, P. Griffith, The syzygy problem, Ann. of Math. 114 (2) (1981) 323–333.
 J.W. Hoffman, H.H. Wang, Castelnuovo–Mumford regularity in biprojective spaces, Adv. Geom. 4 (4) (2004) 513–536.
 H. Knörrer, Cohen–Macaulay modules on hypersurface singularities I, Invent. Math. 88 (1987) 153–164.
 F. Malaspina, Few splitting criteria for vector bundles, Ric. Mat. 57 (2008) 55–64.
 D. Mumford, Lectures on Curves on an Algebraic Surface, Princeton University Press, Princeton, NJ, 1966.
 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 13:32|
|Last Modified:||17 Apr 2012 13:32|
Repository Staff Only: item control page