IPM Calendar 
Monday 22 October 2018   Today  
Events for day: Thursday 11 October 2018    
           08:30 - 18:30     IPM Workshop in APRL
COMSOL Multi-physics General and Specialized Workshop


Farmanieh seminar room C ...

           09:00 - 10:00     Combinatorial Commutative Algebra Weekly Seminar
Stability Properties of Powers of Ideals


Let $R=k[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $k$ and let $I$ be a graded ideal of $R$. Let $astab(I)$, ${astab}(I)$ and $dstab(I)$, respectively, be the smallest integer $n$ for which
$Ass(I^n)$, $Ass({I^n})$ and $depth(I^n)$ stabilize. Here ${I^n}$ denotes the integral closure of $I^n$.

We show that $astab(I)={astab}(I)=dstab(I)$ if $n=2$, while already in $n=3$, $astab(I)$ and ${astab}(I)$ may differ by any amount. Moreover, we show that if $n=4$, then there exist graded ideals $I$ and $J$ such that for any positive integer $c$ one has $astab(I)-dstab(I)geq c$ and $dstab(J)-a ...