|Location:||MSRI: Simons Auditorium|
The Arithmetical Rank of the Edge Ideals of Whisker Graphs
Abstract: A classical problem in Algebraic Geometry consists in finding the minimum number of hypersurfaces that define a certain variety. This problem can be approached from an Algebraic and Combinatorial point of view.
Given a commutative ring R with identity and an ideal I of R, the arithmetical rank of I, denoted ara(I), is the minimum number of elements of R such that the ideal generated by those elements has the same radical as I. The ideal I is called set-theoretic complete intersection (STCI) if ara(I)=ht(I).
In general if I is STCI, then I is Cohen-Macaulay, but the converse is not true. I will show that the converse holds for the edge ideals of some whisker graphs.