FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 2, PAGES 169-184

On nonrational divisors over non-Gorenstein terminal singularities

D. A. Stepanov

Abstract

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Let $(X,o)$ be a germ of a $3$-dimensional terminal singularity of index $m$³ 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 $$C⁴/Z_m is nondegenerate with respect to its Newton diagram. Let $\pi :\; Y\; \to \; X$ be a resolution. We show that there are at most $2$ nonrational divisors $E$_i, $i=1,2$, on $Y$ such that $$p(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.

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Last modified: June 9, 2005