A construction of codimension three arithmetically Gorenstein subschemes of projective space

Transactions of the American Mathematical Society

Volumn 349, Issue 9, 1997, Pages 3803-3821

  Migliore, Juan C ^a   Peterson, Chris ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Arithmetically Gorenstein; Buchsbaum rim complex; Codimension three schemes; Liaison; Linkage; Rank three reflexive sheaves

Indexed keywords

EID: 21944450152     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01978-8     Document Type: Article

References (44)

1. n, Amer. J. of Math. 113 (1991), 117-128. MR 92c:14047
2. D. Bayer and M. Stillman, Macaulay, a computer system for computing in Commutative Algebra and Algebraic Geometry.
3. 5, Math. Ann. 288 (1990), 413-444. MR 91m:14060
4. 5, Complex Projective Geometry, Lond. Math. Soc. Lecture Note Series, 179 (1992), 59-80. MR 94d:14037
5. 4 and deficiency modules, in the proceedings of the conference "Classification of Algebraic Varieties" (L'Aquila 1992), Contemporary Mathematics 162 (1994) (AMS publ.), 49-63. MR 95c:14036
6. G. Bolondi and J. Migliore, Configurations of Linear Projective Subvarieties, in "Algebraic Curves and Projective Geometry, Proceedings (Trento, 1988)," Lecture Notes in Mathematics, vol. 1389, Springer-Verlag (1989), 19-31. MR 90i:14053
7. _, The Lazarsfeld-Rao property on an arithmetically Gorenstein variety, manuscripta math. 78 (1993), 347-368. MR 94a:13008
8. 5, in "Complex Analysis and Geometry," ed. by V. Ancona and A. Silva (1993), Plenum Press, New York, 311-338. MR 94b:14033
9. D. Buchsbaum and D. Eisenbud, Algebra structures for finite free resolutions and some structure theorems for ideals of codimension three, Amer. J. Math. 99 (1977), 447-485. MR 56:11983
10. E. Davis, A.V. Geramita and F. Orecchia, Gorenstein Algebras and the Cayley-Bacharach Theorem, Proc. AMS 93 (1985), 593-597. MR 86k:14034
11. W. Decker, L. Ein and F. Schreyer, Construction of Surfaces in ℙ4, J. Alg. Geom. 2 (1993), 185-237. MR 94a:14037
12. 5, in Vector Bundles in Algebraic Geometry, London Math. Soc. Lecture Note Ser., vol. 208, Cambridge Univ. Press, 1995, pp. 69-100. MR 96d: 14046
13. 4, Invent. Math. 95 (1989), 1-11. MR 89j:14023
14. E.G. Evans and P. Griffith, The Syzygy Problem, Ann. Math. 114 (1981) 323-333. MR 831:13006
15. 3, Comm. Alg. 17 (1989), 3129-3164. MR 90k:14027
16. A.V. Geramita and J. Migliore, Reduced Gorenstein Codimension Three Subschemes of Projective Space, Proc. Amer. Math. Soc. 125 (1997), 943-950.
17. P. Griffiths and J. Harris, Residues and zero-cycles on algebraic varieties, Ann. Math. 108 (1978), 461-505. MR 80d:14006
18. L. Gruson, R. Lazarsfeld and C. Peskine On a theorem of Castelnuovo, and the equations defining space curves, Invent. Math. 72 (1983) 491-506. MR 85g:14033
19. R. Hartshorne, "Algebraic Geometry," Springer-Verlag, Graduate Texts in Mathematics 52 (1977). MR 57:3116
20. _, Stable Reflexive Sheaves, Math. Ann. 254 (1980) 121-176. MR 82b:14011
21. 3 and Zeuthen's Problem, Mem. Amer. Math. Soc. (to appear).
22. C. Huneke, Numerical invariants of liaison classes, Invent, math. 75 (1984), 301-325. MR 85i:13021
23. C. Huneke, B. Ulrich, General Hyperplane Sections of Algebraic Varieties, J. Alg. Geom. 2 (1993), 487-505. MR 94b:14046
24. M. Kreuzer, On 0-dimensional complete intersections, Mathematische Annalen 292 (1992), 43-58. MR 92m:14064
25. M. Kreuzer, "Vektorbündel und der Satz von Cayley-Bacharach," Dissertation, Regensburger Math. Sehr., vol. 21, Universität Regensburg 1989. MR 91d:14035
26. E. Kunz, Almost Complete Intersections are not Gorenstein Rings, J. Alg. 28 (1974), 111-115. MR 48:8496
27. 3, Inv. Math. 91 (1988), 253-258. MR 89g:14027
28. M. Martin-Deschamps and D. Perrin, Sur la Classification des Courbes Gauches, Astérisque 184-185, Soc. Math, de France (1990). MR 91h:14039
29. 5, Proc. A.M.S. 110 (1990), 311-313. MR 91c:14051
30. J. Migliore, Curves and their Hyperplane Sections, lecture notes for the Notre Dame Algebraic Geometry Seminar (1989).
31. Juan Migliore, "An Introduction to Deficiency Modules and Liaison Theory for Subschemes of Projective Space," (monograph) Global Analysis Research Center, Seoul National University, Lecture Notes Series No. 24 (1994). MR 95k:14070
32. N, manuscripta math. 84 (1994), 421-442. MR 95k:14071
33. C. Okonek, M. Schneider and H. Spindler, "Vector Bundles on Complex Projective Space," Birkhauser, Progress in Mathematics 3 (1980). MR 81b:14001
34. C. Peskine and L. Szpiro,' Liaison des variétés algébriques. I, Inv. Math. 26 (1974), 271-302. MR 51:526
35. C. Peterson, Applications of liaison theory to schemes supported on lines, growth of the deficiency module, and low rank vector bundles, Ph.D. thesis, Duke University (1994).
36. S. Popescu and K. Ranestad, Surfaces of degree 10 in Projective Fourspace via Linear Systems and Linkage, J. Alg. Geom. 5 (1996), 13-76. MR 96i:14002
37. D. Portelli and W. Spangher, On the equations which are needed to define a closed subscheme of the protective space, J. Pure and Applied Algebra 98 (1995), 83-93. MR 96d:14002
38. K. Ranestad, Surfaces of degree 10 in the protective fourspace, in "Problems in the Theory of Surfaces and their Classification, Cortona, Italy, 1988," ed. by F. Catanese and C. Ciliberto, Sympos. Math. 32 (1991), 270-307, INDAM, Academic Press, London. MR 95c:14005
39. 3, Invent. Math. 50 (1979), 205-217. MR 80e:14023
40. _ , Liaison Equivalence Classes, Math. Ann. 258 (1981), 169-173. MR 83j:14045
41. R. Re, Sulle sezioni iperpiane di una varietá proiettiva, Le Matematiche (Catania) 42 (1987), 211-218 (1989). MR 90j:14069
42. P. Schenzel, Notes on Liaison and Duality, J. Math, of Kyoto Univ. 22 (1982), 485-498. MR 84a:13012
43. M. Schneider, Boundedness of low-codimensional submanifolds of projective space, Int. J. Math. 3 (3) (1992), 397-399. MR 93g:14057
44. C. Weibel, "An introduction to homological algebra," Cambridge University Press, Cambridge studies in advanced mathematics 38 (1994). MR 95f:18001