Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6414909 | Journal of Algebra | 2013 | 16 Pages |
We investigate local structure of a three dimensional variety X defined over an algebraically closed field k of characteristic p>0 with at most canonical singularities. Under the assumption that p⩾3 and a general hyperplane cut of X has at most rational singularities, we show that local structure of X in codimension two is well understood in the level of local equations. Consequently, we find that i) any singularity of such a variety X in codimension two is compound Du Val, ii) it has a crepant resolution, iii) it is analytically a product of a rational double point and a nonsingular curve when p⩾3 with two exceptions in p=3, and iv) R1ÏâOXË=R1ÏâKXË=0 holds outside some finite points of X for any resolution of singularities Ï:XËâX.