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 $$**C**^{4}/**Z**_{m}
is nondegenerate with respect to its Newton diagram.
Let $\pi :\; Y\; \to \; X$ be a resolution.
We show that there are at most $2$ nonrational
divisors $E$_{i}, $i=1,2$, on $Y$ such that $$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.

Location: http://mech.math.msu.su/~fpm/eng/k05/k052/k05212h.htm

Last modified: June 9, 2005