Resolutions of subsets of finite sets of points in projective space |
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| Authors: | Steven P Diaz Anthony V Geramita Juan C Migliore |
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| Institution: | 1. Department of Mathematics , Syracuse University , Syracuse, N.Y, 13244, USA E-mail: spdiazQmailbox.syr.edu;2. Department of Mathematics and Statistics , Queen's University , Kingston, Ontario, K7L 3N6, Canada E-mail: tonyz@mast. queensu. ca;3. Dipartimento Di Matematica , Universita Di Genova , Genova, Italia E-mail: geramitaQdima.unige.it;4. Department of Mathematics , University of Notre Dame , Notre Dame, 46556, USA E-mail: migliore.lQnd.edu |
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| Abstract: | Abstract Eisenbud et al. proved a number of results regarding Gröbner bases and initial ideals of those ideals J in the free associative algebra K ?X 1,…, X n ? which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one weak notion of generic initial ideals in K ?X 1,…, X n ?, and show that generic initial ideals of ideals containing the anti-commutator ideal, or the commutator ideal, are finitely generated. |
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| Keywords: | Exterior algebra Free associative algebra Gröbner basis Generic initial ideal |
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