Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

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

American Mathematical Society