Article ID Journal Published Year Pages File Type
6414909 Journal of Algebra 2013 16 Pages PDF
Abstract

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) R1π⁎OX˜=R1π⁎KX˜=0 holds outside some finite points of X for any resolution of singularities π:X˜→X.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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