The diagonal subalgebra of a blow-up algebra

Journal of Pure and Applied Algebra

Volumn 125, Issue 1-3, 1998, Pages 305-328

  Simis, A ^a   Trung, N V ^a   Valla, G ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032013177     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(96)00127-2     Document Type: Article

References (25)

1. [1] P.B. Bhattacharaya, The Hilbert function of two ideals, Proc. Cambridge Philos. Soc. 53 (1957) 568-575.
2. [2] A. Björner, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc. 260 (1980) 159-183.
3. [3] N. Bourbaki, Algèbre Commutative (Herrmann, Paris, 1964) Ch. 5.
4. [4] W. Bruns and J. Herzog, On the computation of a-invariants, Manuscripta Math. 77 (1992) 201-213.
5. [5] W. Bruns, A. Simis and N.V. Trung, Blow-up of straightening-closed ideals in ordinal Hodge algebras, Trans. Amer. Math. Soc. 326 (1991) 507-528.
6. [6] W. Bruns and U. Vetter, Determinantal Rings, Lecture notes in Mathematics, Vol. 1327 (Springer, Berlin, Subseries: IMPA, Rio de Janeiro, 1988.)
7. [7] W.-L. Chow, On unmixedness theorem, Amer. J. Math. 86 (1964) 799-822.
8. [8] R. Fröberg and L.T. Hoa, Segre products and Rees algebras of face rings, Comm. Algebra 20(11) (1992) 3369-3380.
9. [9] A.V. Geramita and A. Gimigliano, Generators for the defining ideals of certain rational surfaces, Duke Math. J. 62(1) (1991) 61-83.
10. [10] A.V. Geramita, A. Gimigliano and B. Harbourne, Projectively normal but superabundant embeddings of rational surfaces in projective space, J. Algebra 169(3) (1994) 791-804.
11. [11] A.V. Geramita, A. Gimigliano and Y. Pitteioud, Graded Betti numbers of some embedded rational n-folds, Math. Ann. 301 (1995) 363-380.
12. [12] S. Goto and K. Watanabe, On graded rings I, J. Math. Soc. Japan 30 (1978) 179-213.
13. [13] J. Herzog and N.V. Trung, Gröbner bases and multiplicity of determinantal and Pfaffian ideals, Adv. Math. 96 (1992) 1-37.
14. [14] J. Herzog, N.V. Trung and B. Ulrich, On the multiplicity of blow-up rings of ideals generated by d-sequences, J. Pure Appl. Algebra 80 (1992) 273-297.
15. [15] L.T. Hoa, On Segre products of affine semigroup rings, Nagoya Math. J. 110 (1988) 113-128.
16. [16] M. Hochster and J. Eagon, Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci, Amer. J. Math. 93 (1971) 1020-1058.
17. [17] M. Hochster and J.L. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Adv. Math. 13 (1974) 115-175.
18. [18] S.H. Holay, Generators and resolutions of ideals defining certain surfaces in projective space, Thesis, University of Nebraska, Lincoln, 1994.
19. [19] D. Katz, S. Mandal and J. Verma, Hilbert functions of bigraded algebras, in: A. Simis, N.V. Trung and G. Valla, Eds., Commutative Algebra, Proc. ICTP, Trieste, 1992 (World Scientific, Singapore, 1994).
20. [20] K. Raghavan and A. Simis, Multiplicities of blow-ups of homogeneous quadratic sequences, J. Algebra 175 (1995) 537-567.
21. [21] F.O. Schreyer, Syzygies of canonical curves and special linear series, Math. Ann. 275 (1986) 105-137.
22. [22] A. Simis, Multiplicities and Betti numbers of homogeneous ideals, in: F. Ghione, C. Peskine and E. Sernesi, Eds., Space Curves, Proc. Rocca di Papa 1985, Lecture Notes in Mathematics, Vol. 1266 (Springer, Berlin, 1985).
23. [23] J. Stückrad and W. Vogel, On Segré products and applications, J. Algebra 54 (1978) 374-389.
24. [24] N.V. Trung, Filter regular sequences and multiplicity of blow-up rings of the principal class, J. Math. Kyoto Univ. 33 (1993) 665-683.
25. [25] B.L. van der Waerden, On Hilbert's function, series of composition of ideals and a generalization of a theorem of Bezout, Proc. K. Akad. Amst. 3 (1928) 49-70.