Vol. 9, No. 4, 2015

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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