NOTES ON SYMMETRIC AND EXTERIOR DEPTH AND ANNIHILATOR NUMBERS GESA K ¨ AMPF-MARTINA KUBITZKE

Le Matematiche Vol
2008 unpublished
We survey and compare invariants of modules over the polynomial ring and the exterior algebra. In our considerations, we focus on the depth. The exterior analogue of depth was first introduced by Aramova, Avramov and Herzog. We state similarities between the two notion of depth and exhibit their relation in the case of squarefree modules. Work of Conca, Herzog and Hibi and Trung, respectively, shows that annihila-tor numbers are a meaningful generalization of depth over the polynomial ring. We
more » ... ntroduce and study annihilator numbers over the exterior algebra. Despite some minor differences in the definition, those invariants show common behavior. In both situations a positive linear combination of the annihilator numbers can be used to bound the symmetric and exterior graded Betti numbers, respectively, from above. Entrato in redazione: 2 gennaio 2009
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