Seminario della prof.ssa Susan Cooper - 25 febbraio 2025

Martedì 25 febbraio 2025, ore 10 in aula 126, la prof.ssa Susan Cooper (University of Manitoba, Canada) terrà un seminario dal titolo "Reaping the Benefits of Reduction"
 

Title:  Reaping the Benefits of Reduction

Abstract:  Certain data about a finite set of distinct, reduced points in projective space can be obtained from its Hilbert function. It is well known what these Hilbert functions look like, and it is natural to try to generalize this characterization to non-reduced schemes. In particular, we consider a fat point scheme determined by a set of distinct points (called the support) and non-negative integers (called the multiplicities).  In general, it is not yet known what the Hilbert functions are for fat points with fixed multiplicities as the support points vary.  In this talk we focus on what can be said, in projective 2-space, given information about what collinearities occur among the support points.  Using this information we obtain upper and lower bounds for the Hilbert function of the fat point scheme.  Moreover, we apply a reduction process to give a simple criterion for when the bounds coincide yielding a precise calculation of the Hilbert function in this case.  This is joint work with B. Harbourne and Z. Teitler.