IPM Calendar 
Wednesday 8 December 2021   Today  
Events for day: Thursday 18 November 2021    
           11:00 - 13:00     Commutative Algebra Webinar
On the Hilbert Function of Schemes of Linear Configurations


What is the Hilbert function of a projective scheme X of linear configurations? This is the question we will mainly deal with in this talk. In order to determine the Hilbert function of X in degree d, there is an expected value for it given by a naive count of conditions, which geometrically means that X imposes independent conditions on the linear system of hypersurfaces of degree d containing X. So the question becomes: when does X have the expected Hilbert function, and if it does not, why not? Interestingly enough, there is yet no general answer to it, in fact the problem remains widely open, even in dimX = 2 for re- duced schemes ...