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Shifting Operations and Graded Betti Numbers |
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| Authors: | Annetta Aramova Jürgen Herzog Takayuki Hibi |
| Institution: | (1) Fachbereich Mathematik und Informatik, Universit?t Duisburg-Essen, Campus Essen, DE-45117 Essen, Germany;(2) Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan;(3) Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan |
| Abstract: | The behaviour of graded Betti numbers under exterior and symmetric algebraic shifting is studied. It is shown that the extremal Betti numbers are stable under these operations. Moreover, the possible sequences of super extremal Betti numbers for a graded ideal with given Hilbert function are characterized. Finally it is shown that over a field of characteristic 0, the graded Betti numbers of a squarefree monomial ideal are bounded by those of the corresponding squarefree lexsegment ideal. |
| Keywords: | algebraic shifting shifted complexes generic initial ideals extremal Betti numbers |
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