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Families of curves on surfaces. (English) Zbl 0527.14005

MSC:
14B07 Deformations of singularities
14H10 Families, moduli of curves (algebraic)
14H20 Singularities of curves, local rings
14J10 Families, moduli, classification: algebraic theory
14D15 Formal methods and deformations in algebraic geometry
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
14B05 Singularities in algebraic geometry
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
32S30 Deformations of complex singularities; vanishing cycles
Citations:
Zbl 0516.14023
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References:
[1] Artin, M.: Algebraization of formal moduli. In: Global Analysis. Princeton Univ. Press 1969 · Zbl 0205.50402
[2] Brieskorn, E., Kn?rrer, H.: Ebene algebraische Kurven. Cambridge: Birkh?user 1981
[3] Hartshorne, R.: Algebraic Geometry. Berlin Heidelberg New York: Springer 1977 · Zbl 0367.14001
[4] Mumford, D.: Lectures on curves on an algebraic surface. Ann. of Math Studies59. Princeton: Princeton Univ. Press 1966 · Zbl 0187.42701
[5] Nobile, A.: On families of singular plane projective curves. To appear in Ann. Mat. Pura Appl. (4) · Zbl 0567.14019
[6] Severi, F.: Vorlesungen ?ber algebraische Geometrie. Leipzig: Teubner 1921 · JFM 48.0687.01
[7] Tannenbaum, A.: Families of algebraic curves with nodes. Compositio Math.41, 107-126 (1980) · Zbl 0399.14018
[8] Tannenbaum, A.: Families of curves with nodes on K-3 surfaces. Math. Ann.260, 239-253 (1982) · Zbl 0488.14005
[9] Teissier, B.: Cycles ?vanescents, sections planes, et conditions de Whitney. Asterisque7-8, 285-362 (1973) · Zbl 0295.14003
[10] Wahl, J.: Deformations of plane curves with nodes and cusps. Ann. J. Math.96, 529-577 (1974) · Zbl 0299.14008
[11] Wahl, J.: Equisingular deformations of plane algebroid curves. Trans. Amer. Math. Soc.193, 143-170 (1974) · Zbl 0294.14007
[12] Zariski, O.: Studies in equisingularity, I and II. Amer. J. Math.87, 507-536, 972-1006 (1965) · Zbl 0132.41601
[13] Zariski, O.: Dimension theoretic characterization of maximal irreducible algebraic systems of plane nodal curves of a given ordern and with a given numberd of nodes. Amer. J. Math.104, 209-226 (1982) · Zbl 0516.14023
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