Marinari, Maria Grazia:
Sugli ideali di Borel
Bollettino dell'Unione Matematica Italiana Serie 8 4-B (2001), fasc. n.1, p. 207-237, Unione Matematica Italiana (Italian)
pdf (626 Kb), djvu (408 Kb). | MR1821405 | Zbl 1035.13009
Sunto
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.
Referenze Bibliografiche
[1]
D. BAYER,
The Division Algorithm and the Hilbert Scheme, Ph.D. Thesis, Harvard,
1981. |
MR 2632095[2] A. M. BIGATTI, Aspetti combinatorici e computazionali dell'algebra commutativa, Ph.D. Thesis, Università di Torino, 1995.
[3]
A. M. BIGATTI-
A. V. GERAMITA-
J. MIGLIORE,
Geometric consequences of extremal behaviour in a theorem of Macaulay,
T.A.M.S.,
346 (
1994), 203-235. |
MR 1272673 |
Zbl 0820.13019[5] A. CAPANI-G. NIESI-L. ROBBIANO, CoCoA, a system for doing computation in Commutative Algebra, 1995, available via anonymous ftp from cocoa.dima.unige.it.
[6]
T. DEERY,
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]
D. EISENBUD,
Commutative algebra with a view towards algebraic geometry,
Springer-Verlag,
1995. |
MR 1322960 |
Zbl 0819.13001[8]
S. ELIAHOU-
M. KERVAIRE,
Minimal resolution of some monomial ideals,
J. Algebra,
129 (
1990), 1-25. |
MR 1037391 |
Zbl 0701.13006[9]
J. C. FAUGERE-
P. GIANNI-
D. LAZARD-
T. MORA,
Efficient computation of zero-dimensional Groebner bases by change of ordering,
J. Symbolic Comp.,
16 (
1993), 329-344. |
MR 1263871 |
Zbl 0805.13007[12]
A. GALLIGO,
A propos du Théorem de Préparation de Weierstrass,
L.N. Math.,
409 (
1974), 543-579. |
MR 402102 |
Zbl 0297.32003[13]
M. GREEN,
Generic initial ideals,
Notes from summer School on Commutative Algebra, vol. 2, Barcelona July 1996, 5-85. |
Zbl 0933.13002[14]
H. HULLET,
Maximum Betti numbers of homogeneous ideals with a given Hilbert function,
Comm. Algebra,
21 (7) (
1993), 2335-2350. |
MR 1218501 |
Zbl 0817.13006[15]
M. G. MARINARI-
T. MORA-
H. M. MÖLLER,
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[17] L. RAMELLA, Punti e ideali iniziali generici, Seminario D.I.M.A. Genova, 1998.
[18]
G. VALLA,
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