On the minimal free resolution of general forms |
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Authors: | J Migliore R M Miró -Roig |
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Institution: | Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 ; Facultat de Matemàtiques, Departament d'Algebra i Geometria, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain |
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Abstract: | Let and let be the ideal of generically chosen forms of degrees . We give the precise graded Betti numbers of in the following cases: - ;
- and is even;
- , is odd and ;
- is even and all generators have the same degree, , which is even;
- is even and ;
- is odd, is even, and .
We give very good bounds on the graded Betti numbers in many other cases. We also extend a result of M. Boij by giving the graded Betti numbers for a generic compressed Gorenstein algebra (i.e., one for which the Hilbert function is maximal, given and the socle degree) when is even and the socle degree is large. A recurring theme is to examine when and why the minimal free resolution may be forced to have redundant summands. We conjecture that if the forms all have the same degree, then there are no redundant summands, and we present some evidence for this conjecture. |
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Keywords: | |
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