Self-duality of rank 2 reflexive modules |
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Authors: | Matthew Miller |
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Institution: | Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA |
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Abstract: | Every finitely generated rank 2 third syzygy module over a regular local ring is known to be self-dual. We show more generally that any finitely generated rank 2 reflexive module is self-dual, and that the isomorphism is skew symmetric. We use this ismorphism to estimate how large k may be if the module is a kth syzygy, and how closely allied rank 3 modules are related to their duals. |
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