Sugli ideali di Borel
Marinari, Maria Grazia
Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 207-237 / Harvested from Biblioteca Digitale Italiana di Matematica

In this note we study some algebraic properties of Borel Ideals in the ring of polynomials over an effective field of characteristic zero by using a suitable partial order relation defined on the set of terms of each degree. In particular, in the three variable case, we characterize all the 0-dimensional Borel ideals corresponding to an admissible h-vector and their minimal free resolutions.

Publié le : 2001-02-01
@article{BUMI_2001_8_4B_1_207_0,
     author = {Maria Grazia Marinari},
     title = {Sugli ideali di Borel},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {207-237},
     zbl = {1035.13009},
     mrnumber = {1821405},
     language = {it},
     url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_1_207_0}
}
Marinari, Maria Grazia. Sugli ideali di Borel. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 207-237. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_1_207_0/

[1] Bayer, D., The Division Algorithm and the Hilbert Scheme, Ph.D. Thesis, Harvard, 1981. | MR 2632095

[2] Bigatti, A. M., Aspetti combinatorici e computazionali dell'algebra commutativa, Ph.D. Thesis, Università di Torino, 1995.

[3] Bigatti, A. M.-Geramita, A. V.-Migliore, J., Geometric consequences of extremal behaviour in a theorem of Macaulay, T.A.M.S., 346 (1994), 203-235. | MR 1272673 | Zbl 0820.13019

[4] Bruns, W.-Herzog, J., Cohen-Macaulay rings, Cambridge Press, 1993. | MR 1251956 | Zbl 0788.13005

[5] Capani, A.-Niesi, G.-Robbiano, L., CoCoA, a system for doing computation in Commutative Algebra, 1995, available via anonymous ftp from cocoa.dima.unige.it.

[6] Deery, T., Rev-lex Segment Ideals and minimal Betti numbers, Queen's Papers in Pure and Applied Mathematics. The Curves Seminar, vol. X, 1996. | MR 1381739

[7] Eisenbud, D., Commutative algebra with a view towards algebraic geometry, Springer-Verlag, 1995. | MR 1322960 | Zbl 0819.13001

[8] Eliahou, S.-Kervaire, M., Minimal resolution of some monomial ideals, J. Algebra, 129 (1990), 1-25. | MR 1037391 | Zbl 0701.13006

[9] Faugere, J. C.-Gianni, P.-Lazard, D.-Mora, T., Efficient computation of zero-dimensional Groebner bases by change of ordering, J. Symbolic Comp., 16 (1993), 329-344. | MR 1263871 | Zbl 0805.13007

[10] Floystad, G., A property deducible from the generic initial ideal, to appear in J. of Pure and Applied Algebra. | MR 1674773 | Zbl 0966.13013

[11] Floystad, G.-Green, M., The information encoded in initial ideals, preprint. | MR 1806734 | Zbl 0966.13012

[12] Galligo, A., A propos du Théorem de Préparation de Weierstrass, L.N. Math., 409 (1974), 543-579. | MR 402102 | Zbl 0297.32003

[13] Green, M., Generic initial ideals, Notes from summer School on Commutative Algebra, vol. 2, Barcelona July 1996, 5-85. | Zbl 0933.13002

[14] Hullet, H., Maximum Betti numbers of homogeneous ideals with a given Hilbert function, Comm. Algebra, 21 (7) (1993), 2335-2350. | MR 1218501 | Zbl 0817.13006

[15] Marinari, M. G.-Mora, T.-Möller, H. M., Groebner bases of ideals defined by functionals with an application to ideals of projective points, A. A. E. C. C. vol. 4, n. 2 (1992), 103-145. | MR 1223853 | Zbl 0785.13009

[16] Marinari, M. G.-Ramella, L., Some properties of Borel ideals, accettato a MEGA1998. | MR 1700543 | Zbl 0929.13012

[17] Ramella, L., Punti e ideali iniziali generici, Seminario D.I.M.A. Genova, 1998.

[18] Valla, G., Problems and results on Hilbert functions of graded algebras, Notes from summer School on Commutative Algebra, vol. 1, Barcelona July 1996, 145-211. | Zbl 0946.13012