Title: Regularity of Fat Points

 

Abstract: Every point P in K^n, has an associated ideal I, which consists of the polynomials which vanish on it. Given P, we can define the fat point with weight m, as the ideal I^m. This ideal corresponds to polynomials which vanish on it, and whose m-1 partial derivatives vanish on it as well. The Hilbert function of intersections of these ideals is an interesting topic of study, as it has nice geometric meaning. I will discuss some results and conjectures about Hilbert functions of these ideals and their intersections, as well as discussing some work in progress in the area.