| Abstract: |
Let G be a finite subgroup of SL(n,C), then the quotient C^n/G has a Gorenstein canonical singularity. If n=2 or 3, C^n/G has a crepant resolution. However, in the case n≧4, C^n/G does not always have crepant resolution. In this talk, we show a sufficient condition of existence of crepant resolution for Gorenstein cyclic quotient singularities in all dimensions by using multidimensional continued fractions. Moreover, as a corollary, we prove that all three dimensional Gorenstein abelian quotient singularities possess a crepant resolution. |
