The goal of the talk is to introduce and discuss the notion Koszul algebra in the commutative setting along with the associated notions of G-quadraticity and Koszul filtration. We present some results that appear in the papers [C, CTV, CRV] joint with M.E.Rossi, N.V.Trung and G.Valla. These results concern Koszul and G-quadratic properties of algebras associated with points, curves, cubics and spaces of quadrics of low codimension.
@article{BUMI_2008_9_1_2_429_0, author = {Aldo Conca}, title = {Algebre di Koszul}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {1}, year = {2008}, pages = {429-437}, zbl = {1181.13012}, mrnumber = {2424302}, language = {it}, url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_2_429_0} }
Conca, Aldo. Algebre di Koszul. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 429-437. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_2_429_0/
[A] A counterexample to a conjecture of Serre, Ann. of Math. (2), 115, no. 1 (1982), 1-33. | MR 644015 | Zbl 0454.55004
,[BHV] Syzygies and walks, ICTP Proceedings `Commutative Algebra', Eds. , , , World Scientific 1994, 36-57. | MR 1421076
- - ,[B] A distributiveness property of augmented algebras and some related homological results, Ph.D. thesis, Stockholm University, 1982.
,[BF] Poincarè series of short Artinian rings. J. Algebra, 96, no. 2 (1985), 495-498. | MR 810542
- ,[BF1] Veronese subrings, Koszul algebras and rings with linear resolutions. Rev. Roum. Pures Appl., 30 (1985), 85-97. | MR 789425
- ,[Ca] The pinched Veronese is Koszul. preprint2006, math. AC/0602487. | MR 2563140 | Zbl 1213.13003
,[C] Gröbner bases for spaces of quadrics of low codimension. Adv. in Appl. Math., 24, no. 2 (2000), 111-124. | MR 1748965 | Zbl 1046.13001
,[C1] Gröbner bases for spaces of quadrics of codimension 3, preprint 2007, arXiv:0709.3917. | MR 2517993
,[CRV] Groöbner flags and Gorenstein algebras. Compositio Math., 129, no. 1 (2001), 95-121. | MR 1856025 | Zbl 1030.13005
- - ,[CTV] Koszul property for points in projective spaces, Math. Scand., 89 no. 2 (2001), 201-216. | MR 1868173 | Zbl 1025.13003
- - ,[ERT] Initial ideals, Veronese subrings, and rates of algebras, Adv. Math., 109 (1994), 168-187. | MR 1304751 | Zbl 0839.13013
- - ,[F] Koszul algebras, in "Advances in Commutative Ring Theory", Proc. Fez Conf. 1997, Lecture Notes in Pure and Applied Mathematics, volume 205, Dekker Eds., 1999.
,[HHR] Strongly Koszul algebras, Math. Scand., 86, no. 2 (2000), 161-178. | MR 1754992 | Zbl 1061.13008
- - ,[K] Syzygies for points in projective space, J. Algebra, 145 (1992), 219-223. | MR 1144669 | Zbl 0748.13006
,[PP] Canonical ring of a curve is Koszul: a simple proof, Illinois J. Math., 41, no. 2 (1997), 266-271. | MR 1441677 | Zbl 0916.14013
- ,[P] On the Koszul property of the homogeneous coordinate ring of a curve, J. Algebra, 178, no. 1 (1995), 122-135. | MR 1358259 | Zbl 0861.14030
,[P2] Koszul configurations of points in projective spaces. J. Algebra, 298, no. 1 (2006), 273-283. | MR 2215128 | Zbl 1100.13014
,[R] A description of the homological behaviour of families of quadratic forms in four variables, in Syzygies and Geometry, Boston 1995, , and eds., pp. 86-95, Northeastern Univ. 1995.
,[RS] A toric ring with irrational Poincaré-Betti series, C. R. Acad. Sci. Paris Sér. I Math., 326, no. 2 (1998), 141-146. | MR 1646972 | Zbl 0934.14033
- ,[S] 11, Springer, 1965. | MR 201468
, Algébre locale. Multiplicités, Lecture Notes in Mathematics[VF] The coordinate ring of general curve of genus is Koszul, J. Algebra, 162, no. 2 (1993), 535-539. | MR 1254790 | Zbl 0819.14008
- ,