Smoothness, semistability, and toroidal geometry

Journal of Algebraic Geometry

Volumn 6, Issue 4, 1997, Pages 789-801

  Abramovich, D ^a   De Jong, A J ^b  

^a USA   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944435825     PISSN: 10563911     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. [N] D. Abramovich, A high fibered power of a family of varieties of general type dominates a variety of general type, Inventiones Math., to appear.
2. [N-K] D. Abramovich and K. Karu, Semistable reduction in characteristic 0, preprint.
3. [K-W] D. Abramovich and J. Wang, Equivariant resolution of singularities in characteristic 0, Math. Res. Letters, to appear.
4. [B-M1] E. Bierstone and P. Milman, A simple constructive proof of canonical resolution of singularities. Effective methods in algebraic geometry (Castiglioncello, 1990), 11-30,
5. Progr. Math. 94, Birkhäuser, Boston, MA, 1991.
6. [B-M2] E. Bierstone and P. Milman, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Inventiones Math., to appear.
7. [B-P] F. Bogomolov and T. Pantev, Weak Hironaka theorem, Math. Res. Lett. 3 (1996), No. 3, 299-307.
8. [DM] P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publications Mathématiques 36, 75-109 (1969).
9. [H] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero: I, II, Ann. of Math. (2) 79 (1964), 109-326.
10. [dJ] A. J. de Jong, Smoothness, semistability, and alterations, Inst. Hautes Études Sci. Publ. Math., to appear.
11. [dJ2] A. J. de Jong, Families of curves and alterations, Annales de l'Institute Fourier, to appear.
12. [dJ-O] A. J. de Jong and F. Oort, On extending families of curves, J. Algebraic Geom. 6 (1977) 545-562.
13. [J] J.-P. Jouanolou, Théorèmes de Bertini et Applications, Progress in Math. 42, Birkhäuser: Boston, Basel, Stuttgart, 1983.
14. [K] K. Kato, Toric singularities, Amer. J. Math. 116 (1994), No. 5, 1073-1099.
15. [KKMS] G. Kempf, F. Knudsen, D. Mumford, and B. Saint-Donat, Toroidal Embeddings I, Springer Lecture Notes in Math., No. 339, 1973.
16. [PJ] M. Pikaart and A. J. de Jong, Moduli of curves with non-abelian level structures, in: The moduli spaces of curves, R. Dijkgraaf, C. Faber, G. van der Geer (eds.), Birkhäuser, Boston-Basel-Berlin, Progress in Math. 129 (1995) 483-509.
17. [RG] M. Raynaud and L. Gruson, Critères de platitude et de projectivité, Techniques de ≪platification≫ d'un module, Inventiones Mathematicae 13 (1971) 1-89.
18. [V] O. Villamnyor,Constructiveness of Hironaka's resolution. Ann. Sci. École Norm. Sup. (4) 22 (1989), No. 1, 1-32.