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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

IMPACT FACTOR increased in 2015: 1.616
5-year IMPACT FACTOR: 1.690
Rank 18 out of 312 in category Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 3.614
Source Normalized Impact per Paper (SNIP) 2015: 1.901
Impact per Publication (IPP) 2015: 1.302

Mathematical Citation Quotient (MCQ) 2015: 1.53

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Extending families of curves over log regular schemes

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 1999, Issue 511, Pages 43–71, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.1999.511.43, June 2008

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In this paper, we generalize to the “log regular case” a result of de Jong and Oort which states that any morphism satisfying certain conditions from the complement of a divisor with normal crossings in a regular scheme to a moduli stack of stable curves extends over the entire regular scheme. The proof uses the theory of “regular log schemes” — i.e., schemes with singularities like those of toric varieties – due to K. Kato ([12]). We then use this extension theorem to prove that under certain natural conditions any scheme which is a successive fibration of smooth hyperbolic curves may be compactified to a successive fibration of stable curves.

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