Numerical characters of graded algebras
Valla, Giuseppe
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 257-274 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

This is the summary of the plenary talk I gave in Milan at the XVII Meeting of the Unione Matematica Italiana. We focus on some relevant numerical characters of the standard graded algebras and, in some case, we explain their geometric meaning.

Questo è il sunto della conferenza da me tenuta a Milano in occasione del XVII Congresso UMI. Si introducono alcuni importanti caratteri numerici delle algebre graduate, se ne studiano il comportamento e, in certi casi, la loro rilevanza geometrica.

Publié le : 2004-06-01
@article{BUMI_2004_8_7B_2_257_0,
     author = {Giuseppe Valla},
     title = {Numerical characters of graded algebras},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {257-274},
     zbl = {1177.13035},
     mrnumber = {2072937},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_2_257_0}
}

Valla, Giuseppe. Numerical characters of graded algebras. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 257-274. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_2_257_0/

[1] Alexander, J.-Hirschowitz, A., La méthod d'Horace éclaté: Application à l'interpolation en degré quatre, Inv. Math., 107 (1992), 585-602. | MR 1150603 | Zbl 0784.14002

[2] Anick, D., Thin algebras of embedding dimension three, J. Algebra, 100 (1986), 235-259. | MR 839581 | Zbl 0588.13013

[3] Bayer, D.-Stillman, M., A criterion for detecting m-regularity, Invent. Math., 87 (1987), 1-11. | MR 862710 | Zbl 0625.13003

[4] Bigatti, A. M., Upper bounds for the Betti numbers of a given Hilbert Function, Comm. Algebra, 21 (7) (1993), 2317-2334. | MR 1218500 | Zbl 0817.13007

[5] Brignone, M.-Valla, G., On the resolutions of certain level algebras, preprint (2003). | MR 2102446 | Zbl 1116.13009

[6] Bruns, W.-Herzog, J., Cohen-Macaulay rings, Cambridge studies in advanced mathematics, 39, 1993. | MR 1251956 | Zbl 0788.13005

[7] Buchberger, B., An algorithmic criterion for the solvability of algebraic system of equations, Aequationes Math., 4 (1970), 374-383. | Zbl 0212.06401

[8] Capani, A.-Niesi, G.-Robbiano, L., A system for doing Computations in Commutative Algebra (1995). Available via anonymous ftp from cocoa.dima.unige.it

[9] Cavaliere, M. P.-Rossi, M. E.-Valla, G., The Green-Lazarsfeld conjecture for n+4 points in Pn, Rend. Sem. Mat. Univ. Politec. Torino, 49 (1991), 175-195. | MR 1219266 | Zbl 0796.14028

[10] Charalambous, H.-Evans, E. G., Resolutions with a given Hilbert Function, Contemporary Math., 159 (1994), 19-26. | MR 1266176 | Zbl 0799.18009

[11] De Negri, E.-Valla, G., The h-vector of a Gorenstein codimension three domain, Nagoya Math. J., 138 (1995), 113-140. | MR 1339945 | Zbl 0838.13010

[12] Eisenbud, D.-Goto, S., Linear free resolutions and minimal multiplicity, J. Algebra, 88 (1984), 89-133. | MR 741934 | Zbl 0531.13015

[13] Eisenbud, D.-Popescu, S., The projective geometry of the Gale transform, J. Algebra, 230 (2000), 127-173. | MR 1774761 | Zbl 1060.14528

[14] Fröberg, R., An inequality for Hilbert series of graded algebras, Math. Scand., 56 (1985), 117-144. | MR 813632 | Zbl 0582.13007

[15] Green, M., Koszul cohomology and the Geometry of projective varieties, J. Diff. Geom. (1984), 125-171. | MR 739785 | Zbl 0559.14009

[16] Green, M., Generic Initial ideals, Six Lectures on Commutative Algebra (Bellaterra), Progr. Math.166, Birkhäuser Basel (1998), 119-186. | MR 1648665 | Zbl 0933.13002

[17] Gruson, L.-Peskine, C., Genre des courbes de l'espace projectif, Algebraic Geometry, Lect. Notes Math., 687 (1978), Springer. | MR 527229 | Zbl 0412.14011

[18] Gruson, L.-Lazarsfeld, R.-Peskine, C., On a theorem of Castelnuovo and the equations defining space curves, Inv. Math., 72 (1983), 491-506. | MR 704401 | Zbl 0565.14014

[19] Hulett, H. A., Maximum Betti numbers of homogeneous ideal with a given Hilbert Function, Comm. Algebra, 21 (7) (1993), 2335-2350. | MR 1218501 | Zbl 0817.13006

[20] Kleiman, S., Les théoremes de finitude pour le foncteur de Picard, Exposè XIII. In Théorie des Intersections et Théorem de Riemann-Roch (SGA VI), Springer Lect. Notes in Math., 225 (1971), 616-666. | MR 354655 | Zbl 0227.14007

[21] Lorenzini, A. M., The minimal resolution conjecture, J. Algebra, 156 (1993), 5-35. | MR 1213782 | Zbl 0811.13008

[22] Lazarsfeld, R., A sharp Castelnuovo bound for smooth surfaces, Duke Math. J., 55 (1987), 423-429. | MR 894589 | Zbl 0646.14005

[23] Macaulay, F. S., Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc., 26 (1927), 531-555. | JFM 53.0104.01

[24] Mcduff, D.-Polterovich, L., Symplectic packings and Algebraic Geometry, Inv. Math., 115 (1994), 405-429. | MR 1262938 | Zbl 0833.53028

[25] Rossi, M. E.-Trung, N. V.-Valla, G., Castelnuovo-Mumford regularity and extended degree, Trans. Amer. Math. Soc., 355, no. 5 (2003), 1773-1786. | MR 1953524 | Zbl 1075.13008

[26] Srinivas, V.-Trivedi, V., On the Hilbert Function of a Cohen-Macaulay ring, J. Algebraic Geom., 6 (1997), 733-751. | MR 1487234 | Zbl 0957.13009

[27] Stanley, R., Hilbert Functions of graded algebras, Adv. in Math., 28 (1978), 57-83. | MR 485835 | Zbl 0384.13012

[28] Stanley, R., The Upper Bound conjecture and Cohen-Macaulay rings, Studies in Appl. Math., 54 (1975), 135-142. | MR 458437 | Zbl 0308.52009