The Weak and Strong Lefscahetz properties for Artinian K-algebras

Journal of Algebra

Volumn 262, Issue 1, 2003, Pages 99-126

  Harima, Tadahito ^a   Migliore, Juan C ^b   Nagel, Uwe ^c,e   Watanabe, Junzo ^d  

^a SHIKOKU UNIVERSITY   (Japan)

^b UNIVERSITY OF NOTRE DAME   (United States)

^c UNIVERSITY OF PADERBORN   (Germany)

^d TOKAI UNIVERSITY   (Japan)

^e UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038706396     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(03)00038-3     Document Type: Article

References (29)

1. D. Bayer, M. Stillman, Macaulay: A system for computation in algebraic geometry and commutative algebra, Source and object code available for Unix and Macintosh computers. Contact the authors, or download from ftp://math.harvard.edu via anonymous ftp.
2. A. Bigatti, Upper bounds for the Betti numbers of a given Hilbert function, Comm. Algebra 21 (7) (1993) 2317-2334.
3. A. Bigatti, A.V. Geramita, J. Migliore, Geometric consequences of extremal behavior in a theorem of Macaulay, Trans. Amer. Math. Soc. 346 (1994) 203-235.
4. M. Boij, Components of the space parametrizing graded Gorenstein Artin algebras with a given Hilbert function, Pacific J. Math. 187 (1999) 1-11.
5. D. Buchsbaum, D. Eisenbud, Algebra structures for finite free resolution, and some structure theorems for ideals of codimension 3, Amer. J. Math. 99 (1977) 447-485.
6. 3, in: Algebraic Curves and Projective Geometry, Proceedings, Trento, 1988, in: Lecture Notes in Math., Vol. 1389, Springer-Verlag, 1989, pp. 32-42.
7. S. Diesel, Irreducibility and dimension theorems for families of height 3 Gorenstein algebras, Pacific J. Math. 172 (2) (1996) 365-397.
8. L. Ein, Stable vector bundles on projective spaces in char p > 0, Math. Ann. 254 (1980) 53-72.
9. D. Eisenbud, Commutative Algebra with a View toward Algebraic Geometry, in: Grad. Texts Math., Vol. 150, Springer-Verlag, 1995.
10. S. Eliahou, M. Kervaire, Minimal resolutions of some monomial ideals, J. Algebra 129 (1990) 1-25.
11. A.V. Geramita, T. Harima, Y.S. Shin, Extremal point sets and Gorenstein ideals, Adv. Math. 152 (1) (2000) 78-119.
12. P. Gordan, M. Noether, Ueber die algebraischen Formen, deren Hessesche Determinante idensisch veschwindet, Math. Ann. 10 (1878).
13. T. Harima, Characterization of Hilbert functions of Gorenstein Artin algebras with the Weak Stanley property, Proc. Amer. Math. Soc. 123 (1995) 3631-3638.
14. H. Hulett, Maximum Betti numbers of homogeneous ideals with a given Hilbert function, Comm. Algebra 21 (7) (1993) 2335-2350.
15. A. Iarrobino, Associated Graded Algebra of a Gorenstein Artin Algebra, in: Mem. Amer. Math. Soc., Vol. 107, 1994.
16. H. Ikeda, Results on Dilworth and Rees numbers of Artinian local rings, Japan. J. Math. 22 (1996) 147-158.
17. M. Kreuzer, J. Migliore, U. Nagel, C. Peterson, Determinantal Schemes and Buchsbaum-Rim Sheaves, J. Pure Appl. Algebra 150 (2000) 155-174.
18. J. Migliore, C. Peterson, A construction of codimension three arithmetically Gorenstein subschemes of projective space, Trans. Amer. Math. Soc. 349 (1997) 3803-3821.
19. J. Migliore, U. Nagel, Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers, Adv. Math., to appear.
20. J. Migliore, U. Nagel, C. Peterson, Buchsbaum-Rim sheaves and their multiple sections, J. Algebra 219 (1999) 378-420.
21. U. Nagel, Arithmetically Buchsbaum divisors on varieties of minimal degree, Trans. Amer. Math. Soc. 351 (1999) 4381-4409.
22. K. Pardue, Deformation classes of graded modules and maximal Betti numbers, Illinois J. Math. 40 (1996) 564-585.
23. C. Okonek, M. Schneider, H. Spindler, Vector Bundles on Complex Projective Space, in: Progr. Math., Vol. 3, Birkhäuser, 1988.
24. R. Stanley, The number of faces of a simplicial convex polytope, Adv. Math. 35 (1980) 236-238.
25. R. Stanley, Weyl groups, the hard Lefschetz theorem, and the Sperner property, SIAM J. Algebraic Discrete Methods 1 (1980) 168-184.
26. J. Watanabe, The Dilworth number of Artin Gorenstein rings, Adv. Math. 76 (1989) 194-199.
27. J. Watanabe, The Dilworth number of Artinian rings and finite posets with rank function, in: Commutative Algebra and Combinatorics, in: Adv. Stud. Pure Math., Vol. 11, Kinokuniya, North-Holland, Amsterdam, 1987, pp. 303-312.
28. J. Watanabe, A note on complete intersections of height three, Proc. Amer. Math. Soc. 126 (1998) 3161-3168.
29. J. Watanabe, A remark on the Hessian of homogeneous polynomials, in: The Curves Seminar at Queen's, Vol. XIII, 2000.