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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A numerical condition for a deformation of a Gorenstein surface singularity to admit a simultaneous log-canonical model


Author: Tomohiro Okuma
Journal: Proc. Amer. Math. Soc. 129 (2001), 2823-2831
MSC (2000): Primary 14B07; Secondary 14E15, 32S30, 32S45
Published electronically: February 15, 2001
MathSciNet review: 1840084
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Abstract:

Let $\pi \colon X \to T$ be a deformation of a normal Gorenstein surface singularity over the complex number field $\mathbb{C} $. We assume that $T$ is a neighborhood of the origin of $\mathbb{C} $. Then we prove that $\pi$ admits a simultaneous log-canonical model if and only if an invariant $-P_t\cdot P_t$ of each fiber $X_t$ is constant.


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Additional Information

Tomohiro Okuma
Affiliation: Department of Mathematics, Gunma National College of Technology, 580 Toriba, Maebashi, Gunma 371, Japan
Email: okuma@nat.gunma-ct.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05895-6
PII: S 0002-9939(01)05895-6
Keywords: Normal Gorenstein surface singularity, plurigenera, log-canonical model
Received by editor(s): August 10, 1998
Received by editor(s) in revised form: July 15, 1999, November 4, 1999, and February 7, 2000
Published electronically: February 15, 2001
Communicated by: Ron Donagi
Article copyright: © Copyright 2001 American Mathematical Society