Vol. 9, No. 4, 2015

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Horrocks correspondence on arithmetically Cohen–Macaulay varieties

Francesco Malaspina and A. Prabhakar Rao

Vol. 9 (2015), No. 4, 981–1003
Abstract

We describe a vector bundle on a smooth n-dimensional arithmetically Cohen–Macaulay variety in terms of its cohomological invariants Hi(), 1 i n 1, and certain graded modules of “socle elements” built from . In this way we give a generalization of the Horrocks correspondence. We prove existence theorems, where we construct vector bundles from these invariants, and uniqueness theorems, where we show that these data determine a bundle up to isomorphism. The cases of the quadric hypersurface in n+1 and the Veronese surface in 5 are considered in more detail.

Keywords
vector bundles, cohomology modules, Horrocks correspondence, smooth ACM varieties
Mathematical Subject Classification 2010
Primary: 14F05
Secondary: 14J60
Milestones
Received: 6 October 2014
Revised: 23 February 2015
Accepted: 7 April 2015
Published: 30 May 2015
Authors
Francesco Malaspina
Dipartimento di Scienze Matematiche
Politecnico di Torino
Corso Duca degli Abruzzi 24
I-10129 Torino
Italy
A. Prabhakar Rao
Department of Mathematics
University of Missouri – St. Louis
Saint Louis, MO 63121
United States