Compact moduli of plane curves

Duke Mathematical Journal

Volumn 124, Issue 2, 2004, Pages 213-257

  Hacking, Paul ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644262423     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-04-12421-2     Document Type: Article

References (26)

1. g,n (W) for surfaces" in Higher-Dimensional Complex Varieties (Trento, Italy, 1994), de Gruyter, Berlin, 1996, 1-22. MR 1463171
2. [Ar] M. ARTIN, Versal deformations and algebraic stacks, Invent. Math. 27 (1974), 165-189. MR 0399094
3. [AGV1] M. ARTIN, A. GROTHENDIECK, and J. L. VERDIER, eds., Théorie des topos et cohomologie étale des schémas, 1: Théorie des topos, Séminaire de Géométrie Algébrique du Bois-Marie (SGA 4), Lecture Notes in Math. 269, Springer, Berlin, 1972. MR 0354652
4. [AGV2] -, Théorie des topos et cohomologie étale des schémas, 2, Séminaire de Géométrie Algébrique du Bois-Marie (SGA 4), Lecture Notes in Math. 270, Springer, Berlin, 1972. MR 0354653
5. [AGV3] -, Théorie des topos et cohomologie étale des schémas, 3, Séminaire de Géométrie Algébrique du Bois-Marie (SGA 4), Lecture Notes in Math. 305, Springer, Berlin, 1973. MR 0354654
6. [F] W. FULTON, Introduction to Toric Varieties, Ann. of Math. Stud. 131, Princeton Univ. Press, Princeton, 1993. MR 1234037
7. [H1] P. HACKING, A compactification of the space of plane curves, Ph.D. dissertation, Cambridge Univ., Cambridge, 2001, preprint, arXiv:math.AG/0104193
8. [H2] -, Semistable divisorial contractions, J. Algebra 278 (2004), 173-186.
9. [Ha] B. HASSETT, Stable log surfaces and limits of quartic plane curves, Manuscripta Math. 100 (1999), 469-487. MR 1734796
10. [I1] L. ILLUSIE, Complexe cotangent et déformations, I, Lecture Notes in Math. 239, Springer, Berlin, 1971. MR 0491680
11. [I2] -, Complexe cotangent et déformations, II, Lecture Notes in Math. 283, Springer, Berlin, 1972. MR 0491681
12. [I3] L. ILLUSIE, "Cotangent complex and deformations of torsors and group schemes" in Toposes, Algebraic Geometry and Logic (Halifax, Canada, 1971), Lecture Notes in Math 274, Springer, Berlin, 1972, 159-189. MR 0491682
13. [K] Y. KAWAMATA, D-equivalence and K-equivalence, J. Differential Geom. 61 (2002), 147-171. MR 1949787
14. [Ko] J. KOLLÁR, Toward moduli of singular varieties, Compositio Math. 56 (1985), 369-398. MR 0814554
15. [KA] J. KOLLÁR, D. ABRAMOVICH, ET AL., Flips and Abundance for Algebraic Threefolds (Salt Lake City, Utah, 1991), Astérisque 211, Soc. Math. France, Montrouge, 1992. MR 1225842
16. [KM] J. KOLLÁR and S. MORI, Birational Geometry of Algebraic Varieties, Cambridge Tracts in Math. 134, Cambridge Univ. Press, Cambridge, 1998. MR 1658959
17. [KS] J. KOLLÁR and N. I. SHEPHERD-BARRON, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), 299-338. MR 0922803
18. [L] E. LOOIJENGA, Riemann-Roch and smoothings of singularities, Topology 25 (1986), 293-302. MR 0842426
19. [M] M. MANETTI, Normal degenerations of the complex projective plane, J. Reine Angew. Math. 419 (1991), 89-118. MR 1116920
20. [Ma] H. MATSUMURA, Commutative Ring Theory, 2nd ed., Cambridge Stud. Adv. Math. 8, Cambridge Univ. Press, Cambridge, 1989. MR 1011461
21. [Mo] L. J. MORDELL, Diophantine Equations, Pure Appl. Math. 30, Academic Press, London, 1969. MR 0249355
22. [MFK] D. MUMFORD, J. FOGARTY, and F. KIRWAN, Geometric Invariant Theory, 3rd ed., Ergeb. Math. Grenzgeb. (2) 34, Springer, Berlin, 1994. MR 1304906
23. m Action, Astérisque 20, Soc. Math. France, Montrouge, 1974. MR 0376672
24. [R] M. REID, "Young person's guide to canonical singularities" in Algebraic Geometry (Brunswick, Maine, 1985), Proc. Sympos. Pure Math. 46, Part 1, Amer. Math. Soc., Providence, 1987, 345-414. MR 0927963
25. [S1] J. H. M. STEENBRINK, "Mixed Hodge structure on the vanishing cohomology" in Real and Complex Singularities (Oslo, 1976), Sijthoff and Noordhoff, Alphen aan den Rijn, Netherlands, 1977, 525-563. MR 0485870
26. [S2] -, "Mixed Hodge structures associated with isolated singularities" in Singularities (Arcata, Calif., 1981), Proc. Sympos. Pure Math. 40, Amer. Math. Soc., Providence, 1983, 513-536. MR 0713277