ON NONRATIONAL DIVISORS OVER NON-GORENSTEIN TERMINAL SINGULARITIES

摘要

Let (X, o) be a germ of a 3-dimensional terminal singularity of index m ≥ 2. If (X, o) has type cAx/4, cD/3-3, cD/2-2, or cE/2, then we assume that the standard equation of X in C~4/Z_m is nondegenerate with respect to its Newton diagram. Let π: Y→ X be a resolution. We show that there are at most 2 nonrational divisors E_i, i=1,2, on Y such that π(E_i) = o and the discrepancy a(E_i,X) is at most 1. When such divisors exist, we describe them as exceptional divisors of certain blowups of (X, o) and study their birational type.