On the k-normality of projected algebraic varieties

Bulletin of the Brazilian Mathematical Society

Volumn 33, Issue 1, 2002, Pages 27-48

  Alzati, Alberto ^a   Russo, Francesco ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

k normality; Np conditions; Projection

Indexed keywords

EID: 0013499018     PISSN: 16787544     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005740200001     Document Type: Article

References (25)

1. [AR] A. Alzati and F. Russo, Special subhomaloidal systems of quadrics and varieties with one apparent double point, Math. Proc. Camb. Phil. Soc. 133 (2002), to appear.
2. N, N ≥ 4, Annali Mat. Pura e Appl. 147 (1987), 267-301.
3. [BE2] E. Ballico and P. Ellia, On projections of ruled and Veronese surfaces, J. of Algebra 121 (1989), 477-487.
4. [BEL] A. Bertram, L. Ein and R. Lazarsfeld, Vanishing theorems, a theorem of Severi, and the equations defining projective varieties, J. of the A.M.S. 4 (1991), 587-602.
5. [B1] C. Birkenhake, Linear systems on projective spaces, Man. Math. 88 (1995), 177-184.
6. [B2] C. Birkenhake, Non complete linear systems on abelian varieties, Trans. Amer. Math. Soc. 348 (1996), 1885-1908.
7. [C] G. Castelnuovo, Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica, Rend. Circ. Mat. Palermo 7 (1893), 89-110.
8. [ES] L. Ein and N. Shepherd-Barron, Some special Cremona transformations, Amer. J. Math. 11 (1989), 783-800.
9. [E] D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, GTM 150, 1995.
10. [EG] D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), 89-133.
11. [G] M. Green, Koszul cohomology and the geomery of projective varieties, J. Diff. Geometry 19 (1984), 125-171.
12. [GL] M. Green and R. Lazarsfeld, Some results on the syzygies of finite sets and algebraic curves, Compositio Math. 67 (1988), 301-314.
13. [GLP] L. Gruson, R. Lazarsfeld and C. Peskine, On a theorem of Castelnuovo and the equations defining space curves, Inv. Math. 72 (1983), 491-506.
14. [HKS] K. Hulek, S. Katz and F. O. Schreyer, Cremona transformations and syzygies, Math. Z. 209 (1992), 419-443.
15. [K] S. Kwak, Castelnuovo regularity for smooth subvarieties of dimension 3 and 4, J. Algebraic Geom. 7 (1998), 195-206.
16. [L] R. Lazarsfeld, A sharp Castelnuovo bound for smooth surfaces, Duke Math. J. 55 (1987), 423-429.
17. [Me] C. Meadows, Linear systems cut out by quadrics on projections of varieties, J. of Alg. 90 (1984), 198-207.
18. [MR] M. Mella and F. Russo, On Cremona transformations whose fundamental locus is a smooth irreducible surface, preprint 2001.
19. [Mu] D. Mumford, Lectures on curves on an algebraic surface, Ann. Math. Studies 59 (1966).
20. n and of the Grassmann manifold double-struck G sign (k, n), Proc. London. Math. Soc. 32 (1931), 200-221.
21. [SR] J. G. Semple and L. Roth, Introduction to Algebraic Geometry, Oxford University Press, 1949 and 1986.
22. 7, Mathematika 16 (1969), 88-97.
23. 8, Proc. Lond. Math. Soc. 20 (1970), 205-221.
24. [V] P. Vermeire, Some results on secant varieties leading to a geometric flip construction, Comp. Math. 125 (2001), 263-282.
25. [Z] F. L. Zak, Severi varieties, Math. USSR Sb. 54 (1986), 113-127.