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Geometrical properties of sections of Buchsbaum-Rim sheaves

Igor Burban·Hans-Georg Freiermuth
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Abstract

In this survey article we want to discuss a way of constructing arithmetically Gorenstein varieties of high codimension. Consider kernel sheaves B_G of general, generically surjective morphisms G between decomposable bundles on P^n. The top-dimensional part of the zero-locus of a regular section of B_G is Gorenstein if B_G has odd rank. We show how to implement the construction method in the computer algebra system Singular and produce some examples of Gorenstein curves and threefolds in P^6. Finally, we investigate a class of sheaves B_G, where the degeneracy locus of G does not have the expected codimension.

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Igor Burban, Hans-Georg Freiermuth. 2000-10-27. Geometrical properties of sections of Buchsbaum-Rim sheaves. https://arxiv.org/abs/math/0010276

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