Topics in Commutative Algebra and Algebraic Geometry

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This proposal provides support for the research group in commutative algebra and algebraic geometry at the University of Nebraska---Lincoln. R. Wiegand and S. Wiegand will study local rings of finite Cohen-Macaulaytype. R. Wiegand and Marley will consider homological questions in thetheory of local rings. S. Wiegand will study prime ideal structure inNoetherian rings and constructions involving a homomorphic image of acompletion of a Noetherian domain. Harbourne will investigate resolutionsof ideals corresponding to finite sets of points (with multiplicities)in projective space, and related questions. J. Walker will work oncoding theory, including codes over commutative local Artinianrings. M. Walker will investigate connections between algebraicK-theory and motivic cohomology.Often, real life problems involve many unknown parameters which may be related by equations which are impossible to solve exactly. Nonetheless, using the methods of commutative algebra and algebraic geometry, much valuable descriptive information can be gotten about the sets of solutions, if not the exact solutions themselves. Theinvestigations discussed in this project concern central problems in commutative algebra and algebraic geometry. Just as importantly, many of them are continuations of successful collaborationswith researchers at other institutions. Funds provided under this proposal will allow the UNL research group in commutativealgebra and algebraic geometry to continue its active involvement in collaborative research, its success in the professional development of graduate students and its maintenance as a leading researchgroup in these areas.