The Minimal Resolution Conjecture for Projective Space of dimension 4.

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. September 2010. 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.