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Deligne, Pierre; Mumford, D.

The irreducibility of the space of curves of a given genus. (English) Zbl 0181.48803

Publ. Math., Inst. Hautes Étud. Sci. 36, 75-109 (1969).
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Cited in 25 Reviews
Cited in 617 Documents

MathOverflow Questions:

Moduli problem of stable nodal curves over the integers
Number of irreducible and connected components constant in flat families

Keywords:

algebraic geometry
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References:

[1] S. Abhyankar, Resolution of singularities of arithmetical surfaces,Proc. Conf. on Arith. Alg. Geom. at Purdue. 1963. · Zbl 0147.20503
[2] M. Artin, The implicit function theorem in algebraic geometry,Proc. Colloq. Alg. Geom., Bombay, 1968. · Zbl 0199.24603
[3] M. Artin, Some numerical criteria for contractibility,Am. J. Math.,84 (1962), p. 485. · Zbl 0105.14404 · doi:10.2307/2372985
[4] J. Benabou, Thèse, Paris, 1966.
[5] F. Enriques andChisini,Teoria geometrica delle equazioni e delle funzioni algebriche, Bologna, 1918. · JFM 47.0611.02
[6] W. Fulton, Hurwitz schemes and irreducibility of moduli of algebraic curves,Ann. of Math. (forthcoming). · Zbl 0194.21901
[7] J. Giraud,Cohomologie non abélienne, University of Columbia.
[8] A. Grothendieck, Techniques de descente et théorèmes d’existence en géométrie algébrique, IV,Sem. Bourbaki,221, 1960–1961.
[9] R. Hartshorne, Residues and Duality,Springer Lecture Notes,20, 1966.
[10] D. Knutson, Algebraic spaces,Thesis, M.I.T., 1968.
[11] J. Lipman, Rational singularities,Publ. Math. I.H.E.S., no 36 (1969). · Zbl 0181.48903
[12] M. Lichtenbaum, Curves over discrete valuation rings,Am. J. Math.,90 (1968), p. 380. · Zbl 0194.22101 · doi:10.2307/2373535
[13] W. Manger, Die Klassen von topologischen Abbildungen einer geschlossenen Fläche auf sich,Math. Zeit.,44 (1939), p. 541. · Zbl 0019.28203 · doi:10.1007/BF01210672
[14] D. Mumford,Geometric Invariant Theory, Springer-Verlag, 1965. · Zbl 0147.39304
[15] D. Mumford,Notes on seminar on moduli problems, Supplementary mimeographed notes printed at A.M.S. Woods Hole Summer Institute, 1964. · Zbl 0128.15505
[16] D. Mumford, Picard groups of moduli problems,Proc. Conf. on Arith. Alg. Geom. at Purdue, 1963. · Zbl 0154.20702
[17] A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux,Publ. Math. I.H.E.S., no 21.
[18] M. Raynaud, Spécialisation du foncteur de Picard,Comptes rendus Acad. Sci.,264, p. 941 and p. 1001.
[19] I. Šafarevich, Lectures on minimal models,Tata Institute Lectures notes, Bombay, 1966.
[20] M. Schlessinger,Thesis, Harvard.
[21] J.-P. Serre,Rigidité du foncteur de Jacobi d’échelon n 3, app. à l’exposé 17 du séminaire Cartan 60/61.
[22] F. Severi andLöffler,Vorlesungen über algebraische Geometrie, Teubner, 1924.
[23] A. Weil, Modules des surfaces de Riemann,Sém. Bourbaki, 168, 1957–58.
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