Extending Families of Curves over Log Regular Schemes
نویسنده
چکیده
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 ([9]). 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. 1991 Mathematics Subject Classification: Primary subject: 14H10; Secondary Subject: 14E15.
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Log smooth extension of family of curves and semi-stable reduction
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