Algebra & Discrete Mathematics Seminar
Spring 2016 Schedule

Location: Minard 404 (Seminar Room)
Time: Tuesday, 10:00-10:50 a.m.
Organizer: Cătălin Ciupercă
Previous Semesters


9 February 2016

Cătălin Ciupercă: Reduction numbers of equimultiple ideals

Abstract: Let \((A,\mathfrak{m})\) be an unmixed local ring containing a field. If \(J\) is an \( \mathfrak{m}\)-primary ideal with Hilbert-Samuel multiplicity \(\operatorname{e}(J)\), a recent result of Hickel shows that every element in the integral closure of \(J\) satisfies an equation of integral dependence over \(J\) of degree at most \(\operatorname{e}(J)\). We extend this result to equimultiple ideals \(J\) by showing that the degree of such an equation of integral dependence is at most \(c(J)\), which is one of the elements of the so-called multiplicity sequence introduced by Achilles and Manaresi.  As a consequence, if the characteristic of the field contained in \(A\) is zero, it follows that the reduction number of an equimultiple ideal \(J\) with respect to any minimal reduction is at most \(c(J)-1\).









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