The irreducibility of the space of curves of given genus

Pierre Deligne; David Mumford

Publications Mathématiques de l'IHÉS (1969)

  • Volume: 36, page 75-109
  • ISSN: 0073-8301

How to cite

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Deligne, Pierre, and Mumford, David. "The irreducibility of the space of curves of given genus." Publications Mathématiques de l'IHÉS 36 (1969): 75-109. <http://eudml.org/doc/103899>.

@article{Deligne1969,
author = {Deligne, Pierre, Mumford, David},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {algebraic geometry},
language = {eng},
pages = {75-109},
publisher = {Institut des Hautes Études Scientifiques},
title = {The irreducibility of the space of curves of given genus},
url = {http://eudml.org/doc/103899},
volume = {36},
year = {1969},
}

TY - JOUR
AU - Deligne, Pierre
AU - Mumford, David
TI - The irreducibility of the space of curves of given genus
JO - Publications Mathématiques de l'IHÉS
PY - 1969
PB - Institut des Hautes Études Scientifiques
VL - 36
SP - 75
EP - 109
LA - eng
KW - algebraic geometry
UR - http://eudml.org/doc/103899
ER -

References

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  1. [Ab] S. ABHYANKAR, Resolution of singularities of arithmetical surfaces, Proc. Conf. on Arith. Alg. Geom. at Purdue. 1963. Zbl0147.20503
  2. [A1] M. ARTIN, The implicit function theorem in algebraic geometry, Proc. Colloq. Alg. Geom., Bombay, 1968. Zbl0217.04901
  3. [A2] M. ARTIN, Some numerical criteria for contractibility, Am. J. Math., 84 (1962), p. 485. Zbl0105.14404MR26 #3704
  4. [B] J. BENABOU, Thèse, Paris, 1966. 
  5. [E] F. ENRIQUES and CHISINI, Teoria geometrica delle equazioni e delle funzioni algebriche, Bologna, 1918. 
  6. [F] W. FULTON, Hurwitz schemes and irreducibility of moduli of algebraic curves, Ann. of Math. (forthcoming). Zbl0194.21901
  7. [G] J. GIRAUD, Cohomologie non abélienne, University of Columbia. Zbl0135.02401
  8. [Gr] A. GROTHENDIECK, Techniques de descente et théorèmes d'existence en géométrie algébrique, IV, Sem. Bourbaki, 221, 1960-1961. Zbl0236.14003
  9. [H] R. HARTSHORNE, Residues and Duality, Springer Lecture Notes, 20, 1966. Zbl0212.26101MR36 #5145
  10. [K] D. KNUTSON, Algebraic spaces, Thesis, M.I.T., 1968. Zbl0221.14001
  11. [Li] J. LIPMAN, Rational singularities, Publ. Math. I.H.E.S., n° 36 (1969). Zbl0181.48903
  12. [L] M. LICHTENBAUM, Curves over discrete valuation rings, Am. J. Math., 90 (1968), p. 380. Zbl0194.22101MR37 #6284
  13. [Ma] W. MANGER, Die Klassen von topologischen Abbildungen einer geschlossenen Fläche auf sich, Math. Zeit., 44 (1939), p. 541. Zbl0019.28203
  14. [M1] D. MUMFORD, Geometric Invariant Theory, Springer-Verlag, 1965. Zbl0147.39304MR35 #5451
  15. [M2] D. MUMFORD, Notes on seminar on moduli problems, Supplementary mimeographed notes printed at A.M.S. Woods Hole Summer Institute, 1964. 
  16. [M3] D. MUMFORD, Picard groups of moduli problems, Proc. Conf. on Arith. Alg. Geom. at Purdue, 1963. Zbl0187.42801
  17. [N] A. NÉRON, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. I.H.E.S., n° 21. Zbl0132.41403MR31 #3423
  18. [R] M. RAYNAUD, Spécialisation du foncteur de Picard, Comptes rendus Acad. Sci., 264, p. 941 and p. 1001. Zbl0148.41701MR38 #5796a
  19. [Š] I. ŠAFAREVICH, Lectures on minimal models, Tata Institute Lectures notes, Bombay, 1966. 
  20. [Sc] M. SCHLESSINGER, Thesis, Harvard. 
  21. [S] J.-P. SERRE, Rigidité du foncteur de Jacobi d'échelon n ≥ 3, app. à l'exposé 17 du séminaire Cartan 60/61. 
  22. [Se] F. SEVERI and LÖFFLER, Vorlesungen über algebraische Geometrie, Teubner, 1924. JFM48.0687.01
  23. [W] A. WEIL, Modules des surfaces de Riemann, Sém. Bourbaki, 168, 1957-1958. Zbl0084.28102

Citations in EuDML Documents

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  1. Michel Raynaud, Spécialisation du foncteur de Picard
  2. David Mumford, An analytic construction of degenerating curves over complete local rings
  3. Enrico Arbarello, Weierstrass points and moduli of curves
  4. Anders Kock, The stack quotient of a groupoid
  5. Enrico Arbarello, Alcune osservazioni sui moduli delle curve appartenenti ad una data superficie algebrica
  6. Damiano Fulghesu, Filippo Viviani, The Chow ring of the stack of cyclic covers of the projective line
  7. Angelo Vistoli, Alexander duality in intersection theory
  8. Wolfgang K. Seiler, Global moduli for elliptic surfaces with a section
  9. Henri Carayol, Sur la mauvaise réduction des courbes de Shimura
  10. Michel Raynaud, Compactification du module des courbes

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