Mathematics – Commutative Algebra
Scientific paper
2011-05-19
Mathematics
Commutative Algebra
In version 2 numerous typos have been corrected, details have been added in a few places, and local rearrangements have been m
Scientific paper
The generating series of the Bass numbers $\mu^i_R=\mathrm{rank}_k \mathrm{Ext}^i_R(k,R)$ of local rings $R$ with residue field $k$ are computed in closed rational form, in case the embedding dimension $e$ of $R$ and its depth $d$ satisfy $e-d\le 3$. For each such $R$ it is proved that there is a real number $\gamma>1$, such that $\mu^{d+i}_R\ge\gamma\mu^{d+i-1}_R$ holds for all $i\ge 0$, except for $i=2$ in two explicitly described cases, where $\mu^{d+2}_R=\mu^{d+1}_R=2$. New restrictions are obtained on the multiplicative structures of minimal free resolutions of length 3 over regular local rings.
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