Hilbert functions and level algebras

Journal of Algebra

Volumn 241, Issue 2, 2001, Pages 745-758

  Cho, Young Hyun ^a   Iarrobino, Anthony ^b  

^a Seoul National University   (South Korea)

^b NORTHEASTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035880081     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.2001.8787     Document Type: Article

References (28)

1. D. Bayer, The Division Algorithm and the Hilbert Scheme, thesis, Harvard University, Cambridge, MA, 1982.
2. Bigatti A., Geramita A., Migliore J. Geometric consequences of extremal behavior in a theorem of Macaulay. Trans. Amer. Math. Soc. 346:1994;203-235.
3. A. Bigatti, and, A. Geramita, Level algebras, Lex segments and minimal Hilbert functions, preprint, 2001.
4. Boij M. Betti numbers of compressed level algebras. J. Pure Appl. Algebra. 134:1999;111-131.
5. Boij M. Gorenstein Artin algebras and points in projective space. Bull. London Math. Soc. 31:1999;11-16.
6. Bruns W., Herzog J. Cohen-Macaulay Rings. Cambridge Studies in Advanced Mathematics. 39:1993;Cambridge Univ. Press, Cambridge.
7. J. Chipalkatti, and, A. Geramita, On level algebras in codimension two, in preparation.
8. n, J. Algebra, to appear.
9. Clements G., Lindström L. A generalization of a combinatorial theorem of Macaulay. J. Combin. Theory. 7:1969;230-238.
10. Emsalem J., Iarrobino A. Some zero-dimensional generic singularities; finite algebras having small tangent space. Compositio Math. 36:1978;145-188.
11. Fröberg R. An inequality for Hilbert series of graded algebras. Math. Scand. 56:1985;117-144.
12. Fröberg R., Laksov D. Compressed algebras. Greco S., Strano R. Conference on Complete Intersections in Acireale. Lecture Notes in Mathematics. 1092:1984;121-151 Springer-Verlag, Boston/New York.
13. Gasharov V. Extremal properties of Hilbert functions. Illinois J. Math. 41:1997;612-629.
14. Gasharov V. Green and Gotzmann Theorems for polynomial rings with restricted powers of the variables. J. Pure Appl. Algebra. 130:1998;113-118.
15. Gotzmann G. Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes. Math. Z. 158:1978;61-70.
16. Gotzmann G. Some irreducible Hilbert schemes. Math. Z. 201:1989;13-17.
17. Hibi T. Level rings and algebras with straightening laws. J. Algebra. 117:1988;343-362.
18. A. Iarrobino, Ancester ideals of a vector space of forms, preprint, 1975.
19. Iarrobino A. Punctual Hilbert Schemes. A.M.S. Memoirs. 10:1977;American Mathematical Society, Providence.
20. Iarrobino A. Compressed algebras: Artin algebras having given socle degrees and maximal length. Trans. Amer. Math. Soc. 285:1984;337-378.
21. Iarrobino A. Associated Graded Algebra of a Gorenstein Artin Algebra. Memoirs American Mathematical Society. 107:1994;American Mathematical Society, Providence.
22. Iarrobino A. Inverse system of a symbolic power. III. Thin algebras and fat points. Composito Math. 108:1997;319-356.
23. Iarrobino A., Kanev V. Power Sums, Gorenstein Algebras, and Determinantal Loci. Springer Lecture Notes in Mathematics. 1721:1999;Springer, Heidelberg.
24. Iarrobino A., Kleiman S. The Gotzmann theorems and the Hilbert scheme (Appendix C). Power Sums, Gorenstein Algebras, and Determinantal Loci. Springer Lecture Notes in Mathematics. 1721:1999;Springer, Heidelberg. p. 289-312.
25. Macaulay F. H. S. The Algebraic Theory of Modular Systems. 1916;Cambridge Univ. Press, Cambridge.
26. Macaulay F. H. S. Some properties of enumeration in the theory of modular systems. Proc. London Math. Soc. 26:1927;531-555.
27. Mall D. Betti numbers, Castelnuovo Mumford regularity, and generalizations of Macaulay's theorem. Comm. Algebra. 25:1997;3841-3852.
28. Whipple F. On a theorem due to F. S. Macaulay. J. London Math. Soc. 28:1928;431-437.