﻿﻿﻿﻿ IPM Calendar ﻿
 Thursday 27 June 2019
 Events for day: Thursday 11 October 2018
 08:30 - 18:30     IPM Workshop in APRLCOMSOL Multi-physics General and Specialized Workshop School PHYSICS Farmanieh seminar room C ... Read more           09:00 - 10:00     Combinatorial Commutative Algebra Weekly SeminarStability Properties of Powers of IdealsSchool MATHEMATICSLet \$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 ... Read more
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