Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 36-37.Gunnar Carlsson stated a conjecture which gives a lower bound on the rank of a
differential graded module over a polynomial ring with coefficients in algebraically
closed field k when it has a finite dimensional homology over k. Carlsson showed
that this conjecture implies the rank conjecture about free actions on product
of spheres. In this paper, to understand the Carlsson’s conjecture about differential
graded modules, we study the structure of the variety of upper triangular
square zero matrices and the techniques which were investigated by Rothbach to
determine its irreducible components . We hope these varieties could help prove
Carlsson’s conjecture.Şentürk, BerrinM.S