Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter June 12, 2008

Extending families of curves over log regular schemes

  • Shinichi Mochizuki EMAIL logo

Abstract

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.

Received: 1998-03-30
Accepted: 1998-07-30
Published Online: 2008-06-12
Published in Print: 1999-06-25

© Walter de Gruyter

Downloaded on 29.3.2024 from https://www.degruyter.com/document/doi/10.1515/crll.1999.511.43/html
Scroll to top button