Topics on interpolation problems in algebraic geometry

Rendiconti del Seminario Matematico

Volumn 62, Issue 4, 2004, Pages 279-334

  Bocci, C ^a   Miranda, R ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47249114569     PISSN: 03731243     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (52)

1. Alexander J., Singularités imposables en positions géné rale à une hypersurface projective, Compositio Math. 68(1998), 305-354.
2. Alexander J. and Hirschowitz A., La méthode d'Horace éclatée: application à l'interpolation en degré quatre, Inventiones Mathematicae 107(1992), 582-602.
3. 5, J. Algebraic Geometry 1(1992), 411-426.
4. Alexander J. and Hirschowitz A., Polynomial interpolation in several variables, J. Algebraic Geometry 4(1995), 201-222.
5. Alexander J. and Hirschowitz A., Generic hypersurface singularities, Proc. Indian Acad. Sci. Math. Sci. 107 2(1997), 139-154.
6. Alexander J. and Hirschowitz A., An asympotic vanishing theorem for generic unions of multiple points, Inventiones Mathematicae 140(2000), 303-325.
7. Arbarello E. and Cornalba M., Footnotes to a paper of Beniamino Segre, Math. Ann. 256(1981), 341-362.
8. Arbarello E. and M. Cornalba M., Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves, J. Alg. Geom. 5(1996), 705-749.
9. Ballico E., Bocci C. and Fontanari C., Zero-dimensional subschemes of ruled varieties, to appear on CEJM (2003).
10. Bocci C., Special linear systems and special effect varieties, Ph. D. Thesis, University of Torino, Torino 2003.
11. Buckley A. and Zompatori M., Linear systems of plane curves with a composite number of base points of equal multiplicity, Trans. Amer. Math. Soc. 355 2(2003), 539-549.
12. Boyer C. B., A history of mathematics, John Wiley & Sons, Inc., New York 1991.
13. Carlini E., Geometric aspects of some polynomial decompositions, Ph. D. Thesis, University of Pavia, Pavia 2003.
14. Catalisano M. V., Geramita A. V. and Gimigliano A., On the secant varieties to the tangential varieties of a Veronesean, Proc. A. M. S. 130(2001), 975-985.
15. Catalisano M. V., Geramita A. V. and Gimigliano A., Ranks of tensors, secant varieties of Segre varieties and fat points, Linear Algebra Appl. 355(2002), 263-285.
16. 1, preprint (2003).
17. 1 preprint (2003).
18. Catalisano M. V., Geramita A. V. and Gimigliano A., Higher secant varieties of Segre-Veronese varieties, preprint (2003).
19. Chandler K., A brief proof of a maximal rank theorem for generic double points in projective space, Trans. Amer. Math. Soc. 353 5(2001), 1907-1920.
20. Chiantini L., Lectures on the structure of projective embeddings, Rend. Sem. Mat. Univ. e Polit. Torino 64 4(2004), 59-114.
21. Ciliberto C., Geometric aspects of polynomial interpolation in more variables and of Waring's problem, in: "Proceedings of the Third European Congress of Mathematics, I (Barcelona 2000) ", Prog. Math. 201, Birkhäuser, Basel 2001, 289-316.
22. Ciliberto C. and Miranda R., Degenerations of planar linear systems, J. Reine Angew. Math. 501(1998), 191-220.
23. Ciliberto C. and Miranda R., Linear systems of plane curves with base points of equal multiplicity, Trans. Amer. Math. Soc. 352(2000), 4037-4050.
24. Ciliberto C. and Miranda R., The Segre and Harbourne-Hirschowitz conjectures, in: "Applications of algebraic geometry to coding theory, physics and computation (Eilat 2001) ", NATO Sci. Ser. II Math. Phys. Chem. 36, Kluwer Acad. Publ., Dordrecht 2001, 37-51.
25. Ciliberto C. and Miranda R., Matching conditions for degenerating plane curves and applications, in preparation.
26. Ciliberto C., Cioffi F., Miranda R., and Orecchia F., Bivariate Hermite interpolation and linear systems of plane curves with base fat points, Proceedings of The Asian Symposium on Computer Mathematics [ASCM] 2003.
27. De Volder C. and Laface A., On linear systems of P3 through multiple points, math. AG/0311447, preprint (2003).
28. 3 along a most eight general points, math. AG/0401244, preprint (2004).
29. Dent A., Variations on methods of Lorentz and Lorentz for dimensions two and three, Ph. D. Thesis, Colorado State University 2003.
30. Dent A. and Miranda R., Hermite interpolation on toric surfaces, in preparation.
31. Evain L., Une minoration du degré des courbes planes à singularités imposées, Bull. S. M. F. 126(1998), 525-543.
32. Fontanari C., On Waring's problem for many forms and Grassmann defective varieties, J. Pure Appl. Algebra 74 3(2002), 243-247.
33. Geramita A. V., Inverse systems of fat points: Waring's problem, secant varieties of Veronese varieties and parameter spaces for Gorenstein ideals, in: "The Curves Seminar at Queen's, Vol. X (Kingston, 1995) " Queen's Papers in Pure and Appl. Math. 102, Queen's Univ., Kingston, ON 1996, 2-114.
34. Gimigliano A., On linear systems of plane curves, Thesis, Queen's University, Kingston 1987.
35. Hirschowitz A., La méthode d'Horace pour l'interpolation a plusieurs variables, Manuscripta Math. 50(1985), 337-378.
36. Hirschowitz A., Une conjecture pour la cohomologie des diviseurs sur les surfaces rationnelles g énériques, J. Reine Angew. Math. 397(1989), 208-213.
37. Horn R. A. and Johnson C. R., Matrix Analysis, The Press Syndicate of the University of Cambridge, Cambridge 1990.
38. Laface A., On linear systems of curves on rational scrolls, Geom. Dedicata 90(2002), 127-144.
39. 3, preprint (2003).
40. 3, math. AG/0311445, preprint (2003).
41. Laface A. and Ugaglia L., Special linear system on toric varieties, math. AG/0310043, preprint (2003).
42. Lorentz G. G. and Lorentz R. A., Bivariate Hermite interpolation and applications to algebraic geometry, Numer. Math. 57(1990), 669-680.
43. Lorentz R. A., Multivariate Hermite interpolation by algebraic polynomials: a survey, Journal of Computational and Applied Mathematics 122(2000), 167-201.
44. Malone A., The ten-point problem, Master's Paper, Colorado State University 2003.
45. Miranda R., Linear systems of plane curves, Notices AMS 46(1999), 192-202.
46. Mignon T., Systémes linéaires de courbes planes, Thése, Univ. de Nice, Nice 1997.
47. Mignon T., Systémes linéaires de courbes planes à singularités ordinaires imposées, C. R. Acad. Sci. Paris Sér I Math. 327(1998), 651-654.
48. Ran Z., Enumerative geometry of singular plane curves, Inventiones Mathematicae 97(1989), 447-465.
49. Segre B., Alcune questioni su insiemi finiti di punti in geometria algebrica, Atti Convegno Intern. di Geom. Alg. di Torino, Torino 1961, 15-33.
50. Shafarevich I., Basic algebraic geometry 1: varieties in projective space, Springer - Verlag, Berlin 1994 (second edition).
51. Fulton W., Introduction to toric varieties, Princeton University Press, Princeton 1993.
52. Yang S., Linear systems of plane curves through base points of bounded multiplicity, in: "Polynomial Interpolation and Projective Embeddings. Proceedings of the Workshop", Rend. Sem. Mat. Univ. e Polit. Torino (2005), to appear.