Geometrical properties of sections of Buchsbaum-Rim sheaves
Abstract
In this survey article we want to discuss a way of constructing arithmetically Gorenstein varieties of high codimension. Consider kernel sheaves BG of general, generically surjective morphisms G between decomposable bundles on Pn. The top-dimensional part of the zero-locus of a regular section of BG is Gorenstein if BG 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 P6. Finally, we investigate a class of sheaves BG, where the degeneracy locus of G does not have the expected codimension.
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