The behavior of the Hilbert scheme of points under the derived McKay correspondence

In this thesis, we completely determine the image of structure sheaves of zero-dimensional, torus invariant, closed subschemes on the minimal, crepant resolution Y of the Kleinian quotient singularity C²/Z/n under the Fourier-Mukai equivalence of categories, between derived category of coherent sheaves on Y and Z/n-equivariant derived category of coherent sheaves on C². As a consequence, we obtain a combinatorial correspondence between partitions and Z/n-colored skew partitions.Science, Faculty ofMathematics, Department ofGraduat