The Minimal Resolution Conjecture for Projective Space of dimension 4.
The Minimal Resolution (MR) of an Ideal I of S general points in a Projective Space is the one predicted by Anna L.
The Minimal Resolution Conjecture is known and has been verified for Projective Spaces of dimension 2 and 3.
Also there many counter examples for example for 11 points in a Projective Space of dimension 6, 12 points in a Projective Spaces of dimension 7.
However, for Projective Spaces of dimension 4, it is believed to be true but the complete proof has not been written up so far.
F Lauze (see the ref)tackled part of the resolution in his thesis, I have tackled the other part here in this book - my PhD work.
I hope to have the complete proof soon.
I completed my PhD in Pure Mathematics last year i.e.
I studied at l''Universite de Nice-Sophia Antipolis working under Professor Charles Walter in Algebraic Geometry, specifically on the minimal resolution.
Currently, I am working at the University of Nairobi in the School of Mathematics where I am a Lecturer.