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arXiv · 1407.8464

Horrocks Correspondence on ACM Varieties

F. Malaspina·A. P. Rao
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Abstract

We describe a vector bundle $\sE$ on a smooth $n$-dimensional ACM variety in terms of its cohomological invariants $H^i_*(\sE)$, $1\leq i \leq n-1$, and certain graded modules of "socle elements" built from $\sE$. 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 isomorphisms. The cases of the quadric hypersurface in $\mathbb P^{n+1}$ and the Veronese surface in $\mathbb P^5$ are considered in more detail.

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F. Malaspina, A. P. Rao. 2014-07-31. Horrocks Correspondence on ACM Varieties. https://doi.org/10.2140/ant.2015.9.981

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