Resolution of Nonsingularities of Families of Curves

  • Akio Tamagawa

    Kyoto University, Japan


In the present paper, we consider the following problem: For a given closed point x of a special fiber of a generically smooth family XS of stable curves (with dim(S) = 1), is there a covering YX that is generically étale (i.e., étale over the generic fiber(s) of XS, not only over the generic point(s) of X), where Y is also a family of stable curves, such that the image in X of the non-smooth locus of Y contains x? Among other things, we prove that this is affrmative (possibly after replacing S by a finite extension) in the case where S is the spectrum of a discrete valuation ring of mixed characteristic whose residue field is algebraic over Fp.

Cite this article

Akio Tamagawa, Resolution of Nonsingularities of Families of Curves. Publ. Res. Inst. Math. Sci. 40 (2004), no. 4, pp. 1291–1336

DOI 10.2977/PRIMS/1145475448