Castelnuovo function, zero-dimensional schemes and singular plane curves

Journal of Algebraic Geometry

Volumn 9, Issue 4, 2000, Pages 663-710

  Greuel, Gert Martin ^a   Lossen, Christoph ^a   Shustin, Eugenii ^b  

^a University of Koblenz Landau   (Germany)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034420117     PISSN: 10563911     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. Barkats, D., Irréductibilité des variétés des courbes planes à noeuds et à cusps, Preprint, Université de Nice-Sophia-Antipolis (1993).
2. Buchweitz, R.-O. and Greuel, G.-M., The Milnor number and deformations of complex curve singularities, Invent. Math. 58, 241-281 (1980).
3. nℂ{x, y}, Invent. Math. 41, 45-89 (1977).
4. Casas-Alvero, E., Infinitely near imposed singularities and singularities of polar curves, Math. Ann. 287, 429-454 (1990).
5. Chiantini, L. and Sernesi, E., Nodal curves on surfaces of general type, Math. Ann. 307, 41-56 (1997).
6. 2: New applications of Castelnuovo's function, Ann. Univ. Ferrara, Vol. 32, 93-107 (1986).
7. Diaz, S. and Harris, J., Ideals associated to deformations of singular plane curves, Trans. Amer. Math. Soc. 309, 433-468 (1988).
8. Fogarty, J., Algebraic families on an algebraic surface, Amer. J. Math. 90, 511-521 (1968).
9. Greuel, G.-M. and Karras, U., Families of varieties with prescribed singularities, Compositio Math. 69, 83-110 (1989).
10. Greuel, G.-M. and Lossen, C., Equianalytic and equisingular families of curves on surfaces, Manuscripta Math. 91, 323-342 (1996).
11. Greuel, G.-M., Lossen, C., and Shustin, E., Geometry of families of nodal curves on the blown-up projective plane, Trans. Amer. Math. Soc. 350, 251-274 (1998).
12. Greuel, G.-M., Lossen, C., and Shustin, E., Plane curves of minimal degree with prescribed singularities, Invent. Math. 133, 539-580 (1998).
13. Greuel, G.-M., Lossen, C., and Shustin, E., New asymptotics in the geometry of equisingular families of curves, Internat. Math. Res. Notices 13, 595-611 (1997).
14. Greuel, G.-M., Pfister, G., and Schönemann, H., Singular version 1.2 User Manual. In: Reports On Computer Algebra, number 21. Centre for Computer Algebra, University of Kaiserslautern, (1998). http://www.mathematik.uni-kl.de/∼zca/ Singular.
15. Hartshorne, R., Connectedness of the Hilbert scheme, Inst. Hautes Études Sci. Publ. Math. 29, 261-304 (1966).
16. Iarrobino, A., Punctual Hilbert schemes, Mem. Amer. Math. Soc., No. 188 (1977).
17. Iarrobino, A., Hilbert scheme of points: Overview of last ten years, Proceedings of Symposia in Pure Math. 46, 297-320 (1987).
18. 0 degree of sufficiency of plane curves, Singularities, Part 2 (Arcata 1981). Proceedings of Symposia in Pure Math. 40, 155-160 (1983).
19. Lossen, C., New asymptotics for the existence of plane curves with prescribed singularities, Comm. Algebra 27, 3263-3282 (1999).
20. Lossen, C., The geometry of equisingular and equianalytic families of curves on surfaces, Thesis, Univ. Kaiserslautern (1998).
21. Mather, J. N. and Yau S. S.-T., Classification of isolated hypersurface singularities by their moduli algebras, Invent. Math. 69, 243-251 (1982).
22. Nori, M., Zariski conjecture and related problems, Ann. Sci. École Norm. Sup. (4) 16, 305-344 (1983).
23. Nobile, A. and Villamayor, O. E., Equisingular stratifications associated to families of planar ideals, J. Algebra 193, No. 1, 239-259 (1997).
24. Risler, J.-J., Sur les deformations équisingulières d'idéaux, Bull. Soc. Math. France 101, 3-16 (1973).
25. Severi, F., Vorlesungen über algebraische Geometrie, Teubner (1921) resp. Johnson (1968).
26. Shustin, E., Versal deformation in the space of plane curves of fixed degree, Functional Anal. Appl. 21, 82-84 (1987).
27. Shustin, E., On manifolds of singular algebraic curves, Selecta Math. Sov. 10, 27-37 (1991).
28. Shustin, E., Real plane algebraic curves with prescribed singularities, Topology 32, 845-856 (1993).
29. Shustin, E., Smoothness and irreducibility of varieties of algebraic curves with nodes and cusps, Bull. Soc. Math. France 122, 235-253 (1994).
30. Shustin, E., Geometry of equisingular families of plane algebraic curves, J. Algebraic Geom. 5, 209-234 (1996).
31. Shustin, E., Smoothness of equisingular families of plane algebraic curves, International Math. Res. Notices 2, 67-82 (1997).
32. Shustin, E., Gluing of singular and critical points, Topology 37, no. 1, 195-217 (1998).
33. Teissier, B., The hunting of invariants in the geometry of discriminants, In P. Holm, Real and Complex Singularities, Oslo 1976, North Holland (1978).
34. van der Waerden, B. L., Einführung in die algebraische Geometrie, 2nd edition, Springer-Verlag, Berlin, 1973.
35. Wahl, J., Equisingular deformations of plane algebroid curves, Trans. Amer. Math. Soc. 193, 143-170 (1974).
36. Xu, Geng, Ample line bundles on smooth surfaces, J. reine angew. Math. 469, 199-209 (1995).
37. Zariski, O., Algebraic Surfaces, 2nd ed., Springer-Verlag, Berlin, 1971.