Lectures on the structure of projective embeddings

Rendiconti del Seminario Matematico

Volumn 62, Issue 4, 2004, Pages 335-388

  Chiantini, L ^a  

^a UNIVERSITY OF SIENA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44649101788     PISSN: 03731243     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (83)

1. Adlansvik B., Joins and higher secant varieties, Math. Scand. 61(1987), 213-222.
2. Akivis M., Goldberg V. and Landsberg J., Varieties with degenerate Gauss mapping, math. AG/9908079, preprint (1999).
3. Alexander J. and Hirschowitz A., Polynomial interpolation in several variables, J. Alg. Geom. 4(1995), 201-222.
4. Arbarello E., Cornalba M., Griffiths P. and Harris J., Geometry of algebraic curves, Grundl. der Math. 267, Springer-Verlag, Berlin 1985.
5. Arbarello E. and Cornalba M., Footnotes to a paper of B. Segre, Math. Ann. 256(1981), 341-362.
6. Ballico E. and Ciliberto C., On gaussian maps for projective varieties, in: "Geometry of Complex Varieties, Cetraro, June 1990", Mediterranean Press, Rende 1993, 35-54.
7. Bronowski J., The sums of powers as simultaneous canonical expressions, Proc. Camb. Phyl. Soc. 8(1933), 465-469.
8. Bronowski J., Surfaces whose prime sections are hyperelliptic, J. London Math. Soc. 8(1933), 308-312.
9. Carlini E., Geometric aspects of some polynomial decompositions, Ph. D. Thesis, Univ. Pavia, Pavia 2003.
10. Catalano-Johnson M., The possible dimensions of the higher secant varieties, Amer. J. Math. 118(1996), 355-361.
11. Catalano-Johnson M., The homogeneous ideal of higher secant varieties, J. Pure Appl. Alg. 158(2001), 123-129.
12. Catalisano M. V., Geramita A. V. and Gimigliano A., Rank of skew-symmetric tensors and secant varieties of Grassmannians, preprint (2002).
13. Catalisano M. V., Geramita A. V. and Gimigliano A., Rank of tensors, secant varieties of Segre varieties and fat points, Lin. Alg. and Applic. 355(2002), 263-285.
14. 1, preprint (2003).
15. Chiantini L., Chiarli N. and Greco S., Bounding Castelnuovo-Mumford regularity for varieties with good general projection, J. Pure Appl. Alg. 52(2000), 65-74.
16. Chiantini L. and Ciliberto C., Weakly defective varieties, Trans. Amer. Math. Soc. 354(2002), 151-178.
17. Chiantini L. and Ciliberto C., The grassmannians of secant varieties of curves are not defective, Indag. Math. 13(2002), 23-28.
18. Chiantini L. and Ciliberto C., Threefolds with degenerate secant variety: on a theorem of G. Scorza, in: "Geometric and combinatorial aspects of commutative algebra (Messina, 1999) ", Lect. Notes in Pure and Appl. Math. 217, Marcel Dekker, New York 2001, 111-124.
19. Chiantini L. and Ciliberto C., The classification of defective threefolds, mathAG.0312518, preprint (2003).
20. Chiantini L. and Ciliberto C., The classification of (1, k)-defective surfaces, preprint.
21. Chiantini L. and Ciliberto C., On the concept of k-secant order of a variety, preprint.
22. Chiantini L. and Coppens M., Grassmannians of secant varieties, Forum Math. 13(2001), 615-628.
23. Chiantini L., Lopez A. and Ran Z., Subvarieties of generic hypersurfaces in any variety, Math. Proc. Cambr. Phyl. Soc. 130(2002), 259-268.
24. Chipalkatti J., Apolar schemes of algebraic forms, Can. J. of Math., to appear.
25. Ciliberto C., Geometric aspects of polynomial interpolation in more variables and of Waring's problem, in: "European Congress of Mathematics, Vol. I (Barcelona, 2000) ", Progr. Math. 201, Binkenhäuser, Basel 2001, 289-316.
26. 4 avec sept pointes singulieres generiques, C. R. Acad. Sci. Paris 313(1991), 135-137
27. Ciliberto C., Mella M. and Russo F., Varieties with one apparent double point, mathAG/0210008, preprint (2002).
28. Ciliberto C. and Russo Ê F., Varieties with minimal secant degree and linear systems of maximal dimension on surfaces, preprint (2004).
29. Clemens H., Curves in generic hypersurfaces, Ann. Sci. Ec. Norm. Sup. 19(1986), 629-636.
30. Clemens H. and Ran Z., Twisted genus bounds for subvarieties of generic hypersurfaces, Amer. J. Math, to appear.
31. 2, 3-defect, preprint.
32. Dale M., Terracini's lemma and the secant variety of a curve, Proc. London Math. Soc. 49(1984), 329-339.
33. Dale M., On the secant variety of an algebrac surface, University of Bergen, Dept. of Math. preprint n. 33 (1984).
34. Dionisi C. and Fontanari C., Grassmann defectivity á la Terracini, Le Matematiche 56(2001), 245-255.
35. Eisenbud D. and Harris J., Curves in projective spaces, Montreal University Press, Montreal 1982.
36. Enriques F. and Chisini O., Teoria geometrica delle equazioni e delle funzioni algebriche, vol. III, Zanichelli, Bologna 1982.
37. Fantechi B., On the superadditivity of secants defects, Bull. Soc. Math. France 118(1990), 85-100.
38. Fujita T., Projective threefolds with small secant varieties, Sci. Papers College Gen. Ed. Univ. Tokyo 32(1982), 33-46.
39. Fujita T. and Roberts J., Varieties with small secant varieties: the extremal case, Amer. J. of Math. 103 1(1981), 953-976.
40. Fontanari C., Grassmann defective surfaces, to appear on Boll. UMI.
41. Fulton W. and Hansen J., A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings, Ann. of Math. 110(1979), 159-166.
42. Fulton W. and Lazarsfeld R., Connectivity and its application in algebraic geometry, Lect. Notes in Math. 862, Springer-Verlag, Berlin 1981, 26-92.
43. Gallarati D., Alcune osservazioni sopra le varietà i cui spazi tangenti si appoggiano irregolarmente a spazi assegnati, Rend. Accad. Naz. Lincei, 20 VIII (1956), 193-199.
44. Griffiths P. and Harris J., Algebraic geometry and local differential geometry, Ann. Scient. Ec. Norm. Sup. 12(1979), 335-432.
45. Griffiths P. and Harris J., Principles of algebraic geometry, John Wiley and Sons, New York 1994.
46. Hartshorne R., Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag, Berlin 1977.
47. Harris J., Algebraic Geometry: a first course, Graduate Texts in Math. 133, Springer-Verlag, Berlin 1992.
48. Iarrobino A., Kanev Ê V., Power sums, Gorenstein algebras and determinantal loci, Lect. Notes in Math. 1723, Springer-Verlag, Berlin 1999.
49. Kanev V., Chordal varieties of Veronese varieties and catalecticant matrices, math. AG/9804141, preprint 1998.
50. Landsberg J. M., On degenerate secant and tangential varieties and local differential geometry, Duke Math. J. 85(1996), 605-634.
51. Mella M., Singularities of linear systems and the Waring problem, preprint
52. Mezzetti E., Projective varieties with many degenerate subvarieties, Boll. UMI 8B (1994), 807-832.
53. Mezzetti E. and Tommasi O., On projective varieties of dimension n + k covered by k-spaces, Illinois J. Math. 46(2002), 443-465.
54. Mezzetti E. and Tommasi O., Some remarks on varieties with degenerate Gauss image, mathAG/0304127, preprint (2003).
55. ka due a due incidenti e sulla generazione proiettiva di alcune varietà algebriche, Atti R. Ist. Veneto di Scienze, Lettere ed Arti 101(1941-42), 183-196.
56. h (h + 1)-seganti non riempiono lo spazio ambiente, Atti. Accad. delle Scienze di Torino 41(1906), 634-640.
57. Palatini F., Sulle varietà algebriche per le quali sono di dimension minore dell'ordinario, senza riempire lo spazio ambiente, una o alcune delle varietà formate da spazi seganti, Atti. Accad. delle Scienzedi Torino 44(1909), 362-374.
58. Ran Z., The (dimension+2)-secant lemma, Inv. Math. 106(1991), 65-71.
59. Ravi M. S., Determinantal equations for secant varieties of curves, Comm. Alg. 22(1994), 3103-3106.
60. Rogora E., Varieties with many lines, Manuscripta Math. 82(1994), 207-226.
61. Russo F., On a theorem of Severi, Math. Ann. 316(2000), 1-17.
62. Severi F., Intorno aipunti doppi impropri di una superficie generale dello spazio a quattro dimensioni, eaisuoipuntitripliapparenti, Rend. Circ. Mat. Palermo 15(1901), 33-51.
63. 3tangenti si tagliano a due a due, Rend. Circ. Mat. Palermo 25(1908), 193-204.
64. Scorza G., Unproblema sui sistemi lineari di curve appartenenti a una superficie algebrica, Rend. R. Ist. Lombardo 41 2(1908), 913-920.
65. 4tangenti si tagliano a due a due, Rend. Circ. Mat. Palermo 27(1909), 148-178.
66. Scorza G., Sopra una certa classe di varietà razionali, Rend. Circ. Mat. Palermo 28(1909), 400-401.
67. k, Atti Accad. Naz. Lincei 5(1948), 275-280.
68. Segre C, Preliminari di una teoria delle varietá luoghi di spazi, Rend. Circ. Mat. Palermo 30(1910), 87-121.
69. Segre C, Sulle varietà normali a tre dimensioni composte di serie semplici razionali dipiani, Atti. Accad. Sci. Torino 56(1885), 95-115.
70. Segre C, Le superfici degli iperspazi con una doppia infinitá di curvepiane o spaziali, Atti. Accad. Sci. Torino 21(1920), 75-89.
71. Severi F., Intorno aipunti doppi impropri di una superficie generale dello spazio a quattro dimensioni e ai suoi punti tripli apparenti, Rend. Circ. Mat. Palermo 15(1901), 33-51.
72. Shafarevich I. R., Basic algebraic geometry, Grund. Math. Wissen. Einz. 213 Springer-Verlag, Berlin 1974.
73. Soule C, Secant varieties and successive minima, mathAG./0110254, preprint (2001).
74. h (h + 1)-seganti ha dimension minore dell' ordinario, Rend. Circ. Mat Palermo 31(1911), 392-396.
75. Terracini A., Su due problemi, concernenti la determinazione di alcune classi di superficie, considerati da G. Scorza e F. Palatini, Atti Soc. Natur. e Matem. Modena 6 V (1921-22), 3-16.
76. Terracini A., Sulla rappresentazione di coppie di forme ternarie mediante somme di potenze di forme lineari, Atti Matem. Pura Applic. XXIV (1915), 91-100.
77. Togliatti E., Alcuni esempi di superficie algebriche degli iperspazi che rappresentano un'equazione di Laplace, Comm. Math. Helv. 1(1929), 255-272.
78. Vermeire P., Secant varieties and birational geometry, mathAG/9911078, preprint (1999).
79. Voisin C., On linear subspaces contained in the secant variety of projective curves, AG/0110256, preprint (2003).
80. Voisin C., On a conjecture of Clemens on rational curves on hypersurfaces, J. Diff. Geom. 44(1996), 200-214.
81. Xu G., Subvarieties of general hypersurfaces in projective space, J. Diff. Geom. 39(1994), 139-172.
82. Zak F., Tangents and secants of algebraic varieties, Transl. Math. Monogr. 127, Amer. Math. Soc., Providence RI 1993.
83. Zak F., Some properties of dual varieties and their applications in projective geometry, Lect. Notes in Math. 1479, Springer-Verlag, Berlin 1991, 273-280.