Log smooth extension of a family of curves and semi-stable reduction

Author:
Takeshi Saito

Translated by:

Journal:
J. Algebraic Geom. **13** (2004), 287-321

DOI:
https://doi.org/10.1090/S1056-3911-03-00338-2

Published electronically:
December 3, 2003

MathSciNet review:
2047700

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Abstract | References | Additional Information

Abstract: We show that a family of smooth stable curves defined on the interior of a log regular scheme is extended to a log smooth scheme over the whole log regular scheme, if it is so at each generic point of the boundary, under a very mild assumption. We also include a proof of the fact that a log smooth scheme over a discrete valuation ring has potentially a semi-stable model. As a consequence, we show that a hyperbolic polycurve in the sense of Mochizuk over a discrete valuation field has potentially a proper semi-stable model if the characteristic of the residue field is sufficiently large.

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Additional Information

**Takeshi Saito**

Affiliation:
Department of Mathematics, University of Tokyo, Tokyo 153-8914 Japan

Email:
t-saito@ms.u-tokyo.ac.jp

DOI:
https://doi.org/10.1090/S1056-3911-03-00338-2

Received by editor(s):
October 3, 2001

Published electronically:
December 3, 2003