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Courbes stables de genre 2 et leur schéma de modules

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Références bibliographiques

  • [B-L-R] Bosch, S., Lütkebohmert, W., Raynaud, M.: Néron models. Berlin Heidelberg New York: Springer 1990.

    Google Scholar 

  • [Bo] Bosch, S.: Formelle standardmodelle hyperelliptischer Kurven. Math. Ann.251, 19–42, (1980)

    Google Scholar 

  • [B-M-MB] Bost, J.-B., Mestre, J.-F., Moret-Bailly, L.: Sur le calcul explicite des “classes de Chern” des surfaces arithmétiques de genre 2. In: Séminaire sur les pinceaux de courbes elliptiques. (Astérique, vol.183, pp. 69–105) Paris: Soc. Math. Fr. 1990

    Google Scholar 

  • [C] Coleman, R.: Computing stable reductions. In: Goldstein, C. (ed.) Séminaire de théorie des nombres de Paris 1985–1986. (Prog. Math., vol.71, pp. 1–18) Boston Basel Stuttgart: Birkhäuser 1987

    Google Scholar 

  • [D] Deschamps, M.: Réduction semi-stable. In: Séminaire sur les pinceaux de courbes de genre au moins deux. (Astérisque vol.86, 1–34) Paris: Soc. Math. Fr. 1981

    Google Scholar 

  • [D-M] Deligne, P., Mumford, D.: The irreducibility of the space of curves of given genus. Publ. Math. Inst. Hautes Étud. Sci.36, 75–110 (1969)

    Google Scholar 

  • [F-vdP] Fresnel, J., van der Put, M.: Géométrie analytique rigide et applications. (Prog. Math., vol.18), Boston Basel Stuttgart: Birkhäuser 1981

    Google Scholar 

  • [He] Herrlich, F.: Modultheorie hyperelliptischer Mumfordkurven. Math. Ann.274, 283–299, (1986)

    Google Scholar 

  • [Ho] Homma, M.: Automorphisms of prime order of curves. Manuscr. Math.33, 99–109 (1980)

    Google Scholar 

  • [Ig] Igusa, J.I.: Arithmetic variety of moduli for genus two Ann. Math.72, 612–649 (1960)

    Google Scholar 

  • [Li-1] Liu, Q.: Reduction stable des courbes de genre 2 et le schéma de modules\(\overline M _2 \), C.R. Acad. Sci. Paris Sér. I313, 95–98 (1991)

    Google Scholar 

  • [Li-2] Liu, Q.: Modèles minimaux des courbes de genre 2. (preprint 1992)

  • [Lo-1] Lorenzini, D.: Dual graphs of degenerating curves. Math. Ann.287, 135–150 (1990)

    Google Scholar 

  • [Lo-2] Lorenzini, D.: On the group of components of a Néron model. (preprint 1992)

  • [Lø] Lønsted, K.: The singular points of the moduli spaces for smooth curves. Math. Ann.266, 397–402 (1984)

    Google Scholar 

  • [Me] Mestre, J.-F.: Construction de courbes de genre 2 à partir de leurs modules. In: Mora, T., Traverso, C. (eds.) Effective methods in algebraic geometry. (Prog. Math., vol.94) Boston Basel Stuttgart: Birkhäuser 1990

    Google Scholar 

  • [Mo] Mostafa, S.: Die Singularitäten der Modulmannigfaligkeit\(\overline M _g \) (n)der stabilen Kurven vom Geschlechtg≧2 mitn-Teilungspunktstruktur. J. Reine Angew. Math.343, 81–98 (1983)

    Google Scholar 

  • [Mu] Mumford, D.: An enumerative geometry of the moduli space. In: Artin, M., Tate, J. (eds.) Arithmetic and geometry. (Prog. Math., vol.36, 271–328) Boston Basel Stuttgart: Birkhäuser 1983

    Google Scholar 

  • [N] Namikawa, Y.: On the canonical holomorphic map from the moduli space of stabele curves to the Igusa monoidal transform. Nagoya Math. J.52, 197–259 (1973)

    Google Scholar 

  • [N-U] Namikawa, Y., Ueno, K.: The complete classification of fibers in pencils of curves of genus two. Manuscr. Math.9, 143–186 (1973)

    Google Scholar 

  • [Og] Ogg, A.P.: On pencils of curves of genus two. Topology5, 355–362 (1966)

    Google Scholar 

  • [R] Raynaud, M.: Spécialisation du foncteur de Picard. Publ. Math. Inst. Hautes Étud. Sci.38, 27–76 (1970)

    Google Scholar 

  • [S] Serre, J.-P.: Corps locaux, 2ème éd. Paris: Hermann 1968

    Google Scholar 

  • [S-T] Serre, J-P., Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492–516 (1968)

    Google Scholar 

  • [T] Tate, J.: Rigid analytic spaces. Invent. Math.12, 257–289 (1971)

    Google Scholar 

  • [V] Viehweg, E.: Invarianten der degenerierten Fasern in lokalen Familien von Kurven. J. Reine Angew. Math.293, 284–308 (1977)

    Google Scholar 

  • [Xi] Xiao, G.: On the stable reduciton of pencils of curves. Math. Z.203, 379–389 (1990)

    Google Scholar 

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Liu, Q. Courbes stables de genre 2 et leur schéma de modules. Math. Ann. 295, 201–222 (1993). https://doi.org/10.1007/BF01444884

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