Gorenstein quotient singularities of monomial type in dimension three

J. Math. Sci. Univ. Tokyo
Vol. 2 (1995), No. 2, Page 419--440.

Ito, Yukari
Gorenstein quotient singularities of monomial type in dimension three
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Abstract:
In this paper we give an explicit description of the construction of 3-dimensional smooth varieties coming from a crepant resolution of the underlying spaces of quotient singularities $\Bbb C^3/G$, which are defined by certain monomial type finite subgroups $G$ of $SL(3,\Bbb C)$. Moreover, we prove that the topological Euler number of these varieties equals the number of conjugacy classes of the corresponding acting group. The latter constitutes the verification of a part of the physicist's conjecture concerning \lq\lq the orbifold Euler characteristics".

Mathematics Subject Classification (1991): Primary 14b05; Secondary 32S45, 14F45, 14L30, 14M25, 14E35
Mathematical Reviews Number: MR1366564

Received: 1994-11-21