Varieties with one apparent double point

Journal of Algebraic Geometry

Volumn 13, Issue 3, 2004, Pages 475-512

  Ciliberto, Ciro ^a   Mella, Massimiliano ^b   Russo, Francesco ^c  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITY OF FERRARA   (Italy)

^c FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2642576855     PISSN: 10563911     EISSN: None     Source Type: Journal    
DOI: 10.1090/S1056-3911-03-00355-2     Document Type: Article

References (51)

1. [AB] M. Andreatta, E. Ballico, Classification of protective surfaces with small sectional genus: char p ≥ 0, Rend. Sem. Mat. Univ. Padova 84 (1990), 175-193.
2. [AC] A. Arbarello, M. Cornalba, Footnotes to a paper of Beniamino Segre, Math. Ann. 256 (1981), 341-362.
3. [AR] A. Alzati, F. Russo, Special subhomaloidal systems of guadrics and varieties with one apparent double point, Math. Proc. Camb. Phil. Soc. 133 (2002).
4. [Br] J. Bronowski, The sum of powers as canonical expressions, Proc. Cam. Phil. Soc. 29 (1932), 69-82.
5. [CF] F. Campana, H. Flenner, Projective threefolds containing a smooth rational surface with ample normal bundle, J. für die reine un angew. Math. 440 (1993), 77-98.
6. [CC1] L. Chiantini, C. Ciliberto, A few remarks on the lifting theorem, Asterisque 218 (1993), 95-109.
7. [CC2] L. Chiantini, C. Ciliberto, Threefolds with degenerate secant variety: on a theorem of G. Scorza, Marcel Dekker L.N. 217 (2001), 111-124.
8. [CC3] L. Chiantini, C. Ciliberto, Weakly defective varieties, Trans. Amer. Math. Soc. 354 (2002), no. 1, 151-178.
9. [CS] C. Ciliberto, E. Sernesi, Singularities of the theta divisor and congruences of planes, J. Alg. Geom. 1 (1992), 231-250.
10. [DG] V. Di Gennaro, Alcune osservazioni sulle singolarità dello schema di Hilbert che parametrizza le varietà lineari contenute in una varietà proiettiva, Ricerche di Mat. 39 (1990), 259-291.
11. [Ed] W. L. Edge, The number of apparent double points of certain loci, Proc. Cambridge Philos. Soc. 28 (1932), 285-299.
12. [Ei] L. Ein, Varieties with small dual variety I, Invent. Math. 86 (1986), no. 1, 63-74.
13. [ES] L. Ein, N. Shepherd-Barron, Some special Cremona transformations, Amer. J. Math. 111 (1989), no. 5, 783-800.
14. [EH] D. Eisenbud, J. Harris, On varieties of minimal degree, Algebraic Geometry, Bowdoin 1985, Proc. Symp. in Pure Math. 46 (1987), 3-13.
15. [En] F. Enriques, Le superficie algebriche, Zanichelli, Bologna, (1949).
16. 3, Rend. Accad. d'Italia VII-2 (1941), 282-288.
17. 3, Rend. Accad. Naz. Lincei VIII-2 (1947), 276-279.
18. [GH] Ph. Griffiths, J. Harris, Algebraic geometry and local differential geometry, Ann. Scient. Ec. Norm. Sup. 4 12 (1979), 355-432.
19. [Ha] R. Hartshorne, Algebraic Geometry, Springer Graduate Texts in Math., (1977).
20. [Hi] H. Hironaka, On the arithmetic genera and the effective genera of algebraic curves, Mem. Coll. Sci. Univ. Kyoto A 30 (1957), 177-195.
21. [HKS] K. Hulek, S. Katz, F.O. Schreyer, Cremona transformations and syzygies, Math. Z. 209 (1992), 419-443.
22. [Io1] P. Ionescu, Embedded projective varieties of small invariants, Springer L.N.M. 1056 (1984), 142-186.
23. [Io2] P. Ionescu, On varieties whose degree is small with respect to codimension, Math. Ann. 271 (1985), 339-348.
24. [Io3] P. Ionescu, Generalized adjunction and applications, Math. Proc. Camb. Phil. Soc. 99 (1986), 457-472.
25. [Io4] P. Ionescu, Embedded projective varieties of small invariants. II, Rev. Roum. Math. 31 (1986), 539-545.
26. [Io5] P. Ioescu, Embedded projective varieties of small invariants, III, Springer L.N.M. 1417 (1990), 138-154.
27. [Is1] V. A. Iskovskikh, Fano 3-folds I, Math. USSR Izvestija, AMS Translations 11 (1977), 485-527.
28. [Is2] V. A. Iskovskikh, Fano 3-folds II, Math. USSR Izvestija, AMS Translations 12 (1978), 469-506.
29. [K1] S. Kleiman, About the conormal scheme, in Complete intersections (Acireale, 1983), Lecture Notes in Math. 1092, Springer, Berlin,. (1984), 161-197.
30. 2(C). (French) Vector bundles and differential equations (Proc. Conf., Nice, 1979), pp. 145-182, Progr. Math. 7, Birkhäuser (1980), 145-182.
31. 2(C). (French) Vector bundles and differential equations (Proc. Conf., Nice, 1979), pp. 145-182, Progr. Math. 7, Birkhäuser (1980), 145-182.
32. [Li] L. Livorni, Classification of algebraic varieties with sectional genus less than or equal to six. I: rational surfaces, Pacific J. of Math. 113 (1984), 93-114.
33. [LV] R. Lazarsfeld, A. van de Ven, Topics in the geometry of projective space, DMV Seminar 4, Birkhäuser, (1984).
34. [Ma] A. Mattuck, On the symmetric product of a rational surface, Proc. Amer. Math. Soc. 21 (1969), 683-688.
35. [Me] M. Mella, Existence of good divisors on Mukai varieties, J. of Alg. Geom. 8 (1999), 197-206.
36. [MR] M. Mella, F. Russo, On Cremona transformations whose base locus is a smooth irreducible surface, pre-print (2001).
37. [Mez] B. Mezzetti, Projective varieties with many degenerate subvarieties, Boll. Un. Mat. Ital. B (7) 8 (1994), no. 4, 807-832.
38. 5 with a 3-dimensional family of plane curves, Manuscripta Math. 90 (1996), 365-381.
39. [Mo] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. Math. 116 (1982), 133-176.
40. [Mu1] S. Mukai, Biregular classification of Fano threefolds and Fano manifolds of coindex 3, Proc. Nat. Acad. Sci. USA 86 (1989), 3000-3002.
41. [Mu2] S. Mukai, Simple Lie algebra and Legendre variety, preprint (1998) http://www.math.nagoya-u.ac.jp/~mukai
42. [Pi] R. Piene, A proof of Noether's formula for the arithmetic genus of an algebraic surface, Compositio Math. 38 (1979), 113-119.
43. [Ro] E. Rogora, Medodi proiettivi per lo studio di alcune questioni relative alle varietà immerse, Tesi di Dottorato, Università di Roma "La Sapienza", (1993).
44. [Ru] F. Russo, On a theorem of Severi, Math. Ann. 316 (2000), 1-17.
45. 8, Proc. Lond. Math. Soc. 20 (1970), 205-221.
46. [Se] F. Severi, Intorno ai punti 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.
47. k che rappresentano più di k(k -1)/2 equazioni di Laplace linearmente indipendenti, Rend. Circ. Mat. Palermo, 33 (1912).
48. [vdV] A. van de Ven, On the 2-connectedness of very ample divisors on a surface, Duke Math. J. 46 (1979), no. 2, 403-407.
49. [V] M. G. Violo, Varietà con un punto doppio apparente, Tesi di Dottorato, Torino, (1997).
50. [Za1] F. L. Zak, Tangents and secants of algebraic varieties, Translations of Mathematical Monographs 127, Amer. Math. Soc. (1993).
51. [Za2] F. L. Zak, Varieties of small codimension arising from group actions, Addendum to: [LV].