Abstract
We describe a vector bundle on a smooth -dimensional arithmetically Cohen–Macaulay variety in terms of its cohomological invariants , , 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 and the Veronese surface in are considered in more detail.
Citation
Francesco Malaspina. Aroor Rao. "Horrocks correspondence on arithmetically Cohen–Macaulay varieties." Algebra Number Theory 9 (4) 981 - 1003, 2015. https://doi.org/10.2140/ant.2015.9.981
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