MBOYA, Stephen

MUTUKU, Serryanne Wavinya

Student Bio

Stephen Mboya is a young mathematician whose research interest is on Algebraic geometry. Currently, I have been working on deformation and resolution of surface singularities which form the basis of classification of surface and extended to its numerical properties. I am a bona fide student of University of Nairobi whose educational path is as follows: 2014-2018- Bachelor of Science in Mathematics (University of Nairobi), 2018-2020- Masters of Science in Pure Mathematics (University of Nairobi). My research experience is on rational double point singularities and I am looking forward to extend the acquired knowledge in resolving surface singularities in field of characteristic $p>0$.

Project Summary

Project Title: Deformation and Resolution of Surface Singularities.


In this dissertation, we study ADE surface singularities in terms of Dynkin diagram obtained by deforming and resolving the singularity. Using classic invariant theory, we describe how these surface emerge as quotient of \mathbb{C}^2 /\Gamma, where $\Gamma \subseteq SL_2(\CC),$ is a finite subgroup of the group of $2×2$ matrix of determinant $1$ over C. We further describe how these hypersurface embed in \mathbb{C}^3 as an affine varieties. We deform $ A_n$ type singularity and show its relation to McKay-quivers. Finally, we investigate the the exceptional locus of the resolution of the those isolated singularities using sequence of blowup and from this we obtain the corresponding Dynkin diagram of ADE type.