BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:N. V. Trung (Hanoi Institute of Mathematics) DTSTART:20201029T120000Z DTEND:20201029T130000Z DTSTAMP:20260423T021003Z UID:VCAS/13 DESCRIPTION:Title: Mu ltiplicity sequence and integral dependence\nby N. V. Trung (Hanoi Ins titute of Mathematics) as part of IIT Bombay Virtual Commutative Algebra S eminar\n\n\nAbstract\nThe first numerical criterion for integral dependenc e was proved by Rees in 1961 which states that two m-primary ideals $I \\s ubset J$ in an equidimensional and universally catenary local ring $(R\, m )$ have the same integral closure if and only if they have the same Hilber t-Samuel multiplicity. This result plays an important role in Teissier's w ork on the equisingularity of families of hypersurfaces with isolated sing ularities. For hypersurfaces with non-isolated singularities\, one needs a similar numerical criterion for integral dependence of non-$m$-primary i deals. Since the Hilbert-Samuel multiplicity is no longer defined for non- $m$-primary ideals\, one has to use other notions of multiplicities that c an be used to check for integral dependence. A possibility is the multipli city sequence which was introduced by Achilles and Manaresi in 1997 and ha s its origin in the intersection numbers of the Stuckrad-Vogel algorithm. It was conjectured that two arbitrary ideals $I \\subset J$ in an equidime nsional and universally catenary local ring have the same integral closure if and only if they have the same multiplicity sequence. This talk will p resent a recent solution of this conjecture by Polini\, Trung\, Ulrich and Validashti.\n LOCATION:https://researchseminars.org/talk/VCAS/13/ END:VEVENT END:VCALENDAR