Geodesic
Smooth deformations of reduced curves
Sbornik. Mathematics, Tome 24 (1974) no. 4, pp. 537-546 
A. G. Aleksandrov. Smooth deformations of reduced curves. Sbornik. Mathematics, Tome 24 (1974) no. 4, pp. 537-546. http://geodesic.mathdoc.fr/item/SM_1974_24_4_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper it is shown that a complete reduced curve which is locally a complete intersection over an algebraically closed field has a smooth deformation over the complete local ring of formal power series over the field of definition of the curve. Bibliography: 10 titles.

[1] M. Artin, G. Winters, “Degenerate fibres and stable reduction of curves”, Topology, 10:4 (1971), 373–388 | DOI | MR

[2] P. Deligne, “Intersections sur les surfaces régulières”, Lect. Notes in Math., no. 340

[3] P. Deligne, D. Mumford, “The irreducibility of the space of curves of given genus”, Publ. Math. IHES, no. 36

[4] A. Grotendik, O nekotorykh voprosakh gomologicheskoi algebry, IL, Moskva, 1961

[5] L. Illusie, “Complexe cotangent et Déformations, I”, Lect. Notes in Math., no. 239

[6] S. Lichtenbaum, M. Schlessinger, “The cotangent complex of a morfism”, Trans. Amer. Math. Soc., 128:1 (1967) | DOI | MR | Zbl

[7] A. Néron, “Modéles minimaux des variétés abéliennes sur les corps locaux et globaux”, Publ. Math. IHES, no. 21 | MR | Zbl

[8] A. Ogg, “On the pencils of curves of genus two”, Topology, 5:4 (1966), 355–362 | DOI | MR | Zbl

[9] D. Rim, “Formal deformation theory”, Lect. Notes in Math., no. 288

[10] M. Shlessinger, “Funktory na kategorii artinovykh kolets”, Matematika, 15:4 (1971), 115–129