Déformations de courbes planes

 Access to full text

 Full (PDF)

1. [A] G. Albanese - Sulle condizioni perche una curva algebraica riducible si possa considerare come limite di una curva irredicibile, Rend. Circ. Mat. Palermo52 (1928), 105-150. Zbl54.0685.02JFM54.0685.02
2. [A-M] D. Alibert, G. Maltsmotis - Groupe fondamental du complémentaire d'une courbe à points doubles ordinaires, Bull. Soc. Math. France, 102 (1974), 335-351. Zbl0307.14010MR382285
3. [A-C 1] E. Arbarello, M. Cornalba - Su una proprieta notevole dei morphismi di una curva a moduli generali in uno spazio proiettivo, Rend. Sem. Mat. Univ. Pol. Torino, vol. 38, n° 2 (1980), 87-99. Zbl0478.14016MR624390
4. [A-C 2] E. Arbarello - M. Cornalba - Su una congettura di Petri, Comment. Math. Helv.56 (1981), 1-38. Zbl0505.14002MR615613
5. [A-C 3] E. Arbarello, M. Cornalba - Footnotes to a paper of Beniamino Segre, Math. Ann.256 (1982), 341-362. Zbl0454.14023MR626954
6. [A-C 4] E. Arbarello, M. Cornalba - A few remarks about the variety of irreducible plane curves of given degree and genus, Ann. Sc. Ec. Norm. sup., t. 16 (1983), 467-488. Zbl0553.14009MR740079
7. [A-C-G-H] E. Arbarello, M. Cornalba, P. Griffiths, J. Harris - Geometry of algebraic curves, Berlin - Heidelberg - New-York - Tokyo, Springer-Verlag (1984). Zbl0559.14017
8. [A-W] M. Artin, G. Winters - Degenerate fibers and reduction of curves, Topology, 10 (1971) , 373-383. Zbl0196.24403MR476756
9. [D] P. Deligne - Le groupe fondamental du complément d' une courbe plane n'ayant que des points doubles ordinaires est abélien, Sém. Bourbaki, exp. 543 (Nov. 1979), Lecture Notes in Math., 842, Springer-Verlag (1981), 1-10. Zbl0478.14008MR636513
10. [D-M] P. Deligne, D. Mumford - The irreducibility of the space of curves of given genus, Publications IHES15 (1972) , 75-110. MR262240
11. [D-H] S. Diaz, J. Harris - Ideals associated to deformations of singular plane curves, preprint. MR961600
12. [E] D. Eisenbud - Rational curves with cusps, Proceedings of Symposia in Pure Math., Vol. 40, part 1 (1983), 337-344. Zbl0538.14021MR713072
13. [F1] W. Fulton - On the fundamental group of the complement of a node curve, Ann. of Math.111 (1980), 407-409. Zbl0406.14008MR569076
14. [F2] W. Fulton - On nodal curves, in Algebraic geometry : open problems, Lect. Notes997, Springer-Verlag, Berlin-Heidelberg-New York. Zbl0514.14012MR714747
15. [G] G. Giacinti-Diebolt - Variétés des courbes projectives planes de degré et lieu singulier donnés, Math. Annalen266 (1984), 321-350. Zbl0504.14017MR730174
16. [H1] J. Harris - On the Severi problem, Invent. Math.84 (1986), 445-461. Zbl0596.14017MR837522
17. [H2] J. Harris - Curves and their moduli, Notes of lectures given at the AMS Summer Institute in Algebraic Geometry, June 1985 (Sept. 1986). Zbl0646.14019MR927953
18. [K-Kn-M-S] G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat - Toroidal embeddings I, Lecture Notes in Math.339, Springer-Verlag (1973). Zbl0271.14017MR335518
19. [Kn] F. Knudsen - The projectivity of the moduli space of stable curves III, Math. Scand.52 (1983), 200-212. Zbl0544.14021MR702954
20. [L1] I. Luengo - On the existence of complete families of projective plane curves which are obstructed (1985), Journal of the London Mathematical Society36 (1987), 33-43. Zbl0641.14012MR897672
21. [L2] I. Luengo - The μ-constant stratum is not smooth for surface singularities (1985), à paraître aux Inventiones Mathematicae. Zbl0627.32018
22. [M] D. Mumford - Stability of projective varieties, L'Enseignement Mathématique23 (1977), 39-110. Zbl0363.14003MR450272
23. [N1] A. Nobile - On families of singular plane projective curves, Annali di matematica pura ed applicata138 (1984), 341-378. Zbl0567.14019MR779551
24. [N2] A. Nobile - Families of curves on surfaces, Math. Z, 187 (1984), 453- 470. Zbl0527.14005MR760046
25. [N3] A. Nobile - On specializations of curves I, Transactions of the American Mathematical Society282 (1984), 739-748. Zbl0537.14019MR732116
26. [N4] A. Nobile - Genera of curves varying in a family (1987), à paraître aux Annales de l'E.N.S. Zbl0687.14024MR925723
27. [P] H. Popp - Zur Reduktionstheorie algebraischer Funktionenkörper vom Transzendenzgrad 1, Archiv. der Math., Basel17 (1966), 510-522. Zbl0192.26901MR205996
28. [R] Z. Ran - On nodal plane curves, Invent. Math.86 (1986), 529-534. Zbl0644.14009MR860680
29. [Se] B. Segre - Existenza e dimensione di sistemi continui di curve piane algebrische con dati caraterri, Atti Acad. Naz. Lincei Rendicontini, Serie 6, Vol. 10 (1929), 31-38. JFM55.1001.01
30. [S] F. Severi - Vorlesungen über Algebraische Geometrie, Teubner, Leipzig (1921). JFM48.0687.01
31. [T1] A. Tannenbaum - Families of algebraic curves with nodes, Compositio Mathematica, Vol. 41, Fasc. 1 (1980), 107-126. Zbl0399.14018MR578053
32. [T2] A. Tannenbaum - On the classical characteristic linear series of plane curves with nodes and cuspidal points : two examples of Beniamino Segre, Compositio Mathematica, Vol. 51 (1984), 169-183. Zbl0556.14008MR739731
33. [Te] B. Teissier - Résolution simultanée, Séminaire sur les singularités des surfaces, Palaiseau (1976-77), Lectures Notes in Math., 777, Springer-Verlag (1980), 71-146. Zbl0464.14005MR579026
34. [W1] J. Wahl - Deformations of plane curves with nodes and cusps, American Journal of Mathematics, Vol. 96, n° 4 (1974), 529-577. Zbl0299.14008MR387287
35. [W2] J. Wahl - Equisingular deformations of plane algebroid curves, Trans. Amer. Math. Soc.196 (1974), 143-170. Zbl0294.14007MR419439
36. [Z1] O. Zariski - On the problem of existence of algebraic functions of two variables possessing a given branch curve, American J. Math.51 (1929), 305-328. MR1506719JFM55.0806.01
37. [Z2] O. Zariski - Algebraic surfaces, 2nd edition, Springer-Verlag, Heidelberg (1971). Zbl0219.14020MR469915
38. [Z3] O. Zariski - Dimension theoretic - characterization of maximal irreducible algebraic systems of plane nodal curves of a given order n and with a given number d of nodes, American J. of Math.104 (1982), 209-226. Zbl0516.14023MR648487
39. [Z4] O. Zariski - On the problem of irreducibility of the algebraic system of irreducible plane curves of a given order and having a given number of nodes, in Arithmetic and Geometry, Vol. II, Papers dedicated to I.R. Shafarevich, Progress in Mathematics36 (1983), Birkhäuser, 465-481. Zbl0597.14022MR717621

1. Pierre-Henri Chaudouard, Gérard Laumon, [unknown]