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Elliptic singularities and threefold flops in positive characteristic

Part of: Surfaces and higher-dimensional varieties Birational geometry

Published online by Cambridge University Press:  27 May 2025

Hiromu Tanaka
Hiromu Tanaka*
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, Japan
*
Email: tanaka.hiromu.7z@kyoto-u.ac.jp
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Abstract

Let X be a smooth threefold over an algebraically closed field of positive characteristic. We prove that an arbitrary flop of X is smooth. To this end, we study Gorenstein curves of genus one and two-dimensional elliptic singularities defined over imperfect fields.

Keywords

elliptic singularitiesthree-dimensionalterminal singularitiesflopspositive characteristic

MSC classification

Primary: 14J17: Singularities
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 68 , Issue 4 , November 2025 , pp. 1188 - 1244
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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