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Transactions of the American Mathematical Society

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On the resolution of certain graded algebras

Authors: M. P. Cavaliere, M. E. Rossi and G. Valla
Journal: Trans. Amer. Math. Soc. 337 (1993), 389-409
MSC: Primary 13D02; Secondary 14M99
MathSciNet review: 1110573
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Abstract: Let $ A = R/I$ be a graded algebra over the polynomial ring $ R = k[{X_0}, \ldots ,{X_n}]$. Some properties of the numerical invariants in a minimal free resolution of $ A$ are discussed in the case $ A$ is a "Short Graded Algebra". When $ A$ is the homogeneous coordinate ring of a set of points in generic position in the projective space, several result are obtained on the line traced by some conjectures proposed by Green and Lazarsfeld in [GL] and Lorenzini in [L1]

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  • [BG] E. Ballico and A. V. Geramita, The minimal free resolution of the ideal of s general points in $ {{\mathbf{P}}^3}$, Canad. Math. Soc. Conf. Proc., vol. 6, Amer. Math. Soc., Providence, R.I., 1986, pp. 1-9. MR 846012 (87j:14079)
  • [CRV1] M. P. Cavaliere, M. E. Rossi and G. Valla, On short graded algebras, Commutative Algebra, Salvador, vol. 1430, Lecture Notes in Math., Springer, 1990, pp. 21-31. MR 1068321 (91g:13030)
  • [CRV2] -, On the resolution of points in generic position, Comm. Algebra (4) 19 (1991), 1083-1097. MR 1102328 (92g:14048)
  • [CRV3] -, On Green-Lazarsfeld and minimal resolution conjecture for $ n + 3$ points in $ {{\mathbf{P}}^n}$, J. Pure Appl. Algebra (to appear).
  • [ERV] J. Elias, R. Robbiano and G. Valla, Number of generators of ideals, Nagoya Math J. 123 (1991), 39-76. MR 1126182 (92h:13023)
  • [EK] D. Eisenbud and J. H. Koh, Remarks on points in a projective space, Commutative Algebra, Proceedings of a microprogram held June 15-July 2, 1987, vol. 15, Math. Sci. Research Inst. Publ., Springer, 1989, pp. 157-172. MR 1015517 (90i:14008)
  • [EK1] -, Some linear syzygies conjectures, Adv. Math. (to appear).
  • [G] M. Green, Koszul homology and the geometry of projective varieties, J. Differential Geometry 19 (1984), 125-171. MR 739785 (85e:14022)
  • [GL] M. Green and R. Lazarsfeld, Some results on the syzygies of finite sets and algebraic curves, Comput. Math. 67 (1988), 301-314. MR 959214 (90d:14034)
  • [GN] A. Giovini and G. Niesi, CoCoA: A user-friendly system for commutative algebra, design and implementation of symbolic computation systems, 429, Lecture Notes in Comput. Sci., Springer-Verlag, 1990, pp. 20-30.
  • [GO] A. V. Geramita and F. Orecchia, On the Cohen-Macaulay type of s lines in $ {{\mathbf{A}}^{n + 1}}$, J. Algebra 70 (1981), 116-140. MR 618382 (82g:13018)
  • [HSV] L. T. Hoa, J. Stükrad and W. Vogel, Toward a structure theory for projective varieties of degree = codimension $ + 2$, Preprint 1989.
  • [H] J. Harris, Curves in projective space, Séminaire de Mathématiques Supérieures, Université de Montréal, 1982. MR 685427 (84g:14024)
  • [L1] A. Lorenzini, On the Betti numbers of points in the projective space, Thesis, Queen's University, Kingston, Ontario, 1987.
  • [L2] -, Betti numbers of perfect homogeneous ideals, J. Pure Appl. Algebra 60 (1989), 273-288. MR 1021852 (90i:13022)
  • [L3] -, The minimal resolution conjecture, J. Algebra (to appear). MR 1213782 (94g:13005)
  • [MNV] P. Maroscia, U. Nagel and W. Vogel, On degree bound for the syzygies of a finite set of points in $ {{\mathbf{P}}^n}$, Preprint 1990.
  • [TV] N. V. Trung and G. Valla, The Cohen-Macaulay type of points in generic position, J. Algebra 125 (1989), 110-119. MR 1012665 (90i:13009)

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Keywords: Resolutions of graded algebras, Koszul complex, points in generic position, minimal resolution conjecture, Green and Lazarsfeld conjecture
Article copyright: © Copyright 1993 American Mathematical Society

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