Geodesic
Algebre di Koszul
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 2, pp. 429-437.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
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Conca, Aldo. Algebre di Koszul. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 2, pp. 429-437. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_2_a6/

[A] D. Anick, A counterexample to a conjecture of Serre, Ann. of Math. (2), 115, no. 1 (1982), 1-33. | DOI | MR | Zbl

[BHV] W. Bruns - J. Herzog - U. Vetter, Syzygies and walks, ICTP Proceedings `Commutative Algebra', Eds. A. Simis, N. V. Trung, G. Valla, World Scientific 1994, 36-57. | MR

[B] J. Backelin, A distributiveness property of augmented algebras and some related homological results, Ph.D. thesis, Stockholm University, 1982.

[BF] J. Backelin - R. Fröberg, Poincarè series of short Artinian rings. J. Algebra, 96, no. 2 (1985), 495-498. | DOI | MR

[BF1] J. Backelin - R. Fröberg, Veronese subrings, Koszul algebras and rings with linear resolutions. Rev. Roum. Pures Appl., 30 (1985), 85-97. | MR

[Ca] G. Caviglia, The pinched Veronese is Koszul. preprint 2006, math. AC/0602487. | DOI | MR | Zbl

[C] A. Conca, Gröbner bases for spaces of quadrics of low codimension. Adv. in Appl. Math., 24, no. 2 (2000), 111-124. | DOI | MR | Zbl

[C1] A. Conca, Gröbner bases for spaces of quadrics of codimension 3, preprint 2007, arXiv:0709.3917. | DOI | MR

[CRV] A. Conca - M. E. Rossi - G. Valla, Groöbner flags and Gorenstein algebras. Compositio Math., 129, no. 1 (2001), 95-121. | DOI | MR | Zbl

[CTV] A. Conca - N. V. Trung - G. Valla, Koszul property for points in projective spaces, Math. Scand., 89 no. 2 (2001), 201-216. | DOI | MR | Zbl

[ERT] D. Eisenbud - A. Reeves - B. Totaro, Initial ideals, Veronese subrings, and rates of algebras, Adv. Math., 109 (1994), 168-187. | DOI | MR | Zbl

[F] R. Fröberg, 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] J. Herzog - T. Hibi - G. Restuccia, Strongly Koszul algebras, Math. Scand., 86, no. 2 (2000), 161-178. | DOI | MR | Zbl

[K] G. Kempf, Syzygies for points in projective space, J. Algebra, 145 (1992), 219-223. | DOI | MR | Zbl

[PP] G. Pareschi - B. P. Purnaprajna, Canonical ring of a curve is Koszul: a simple proof, Illinois J. Math., 41, no. 2 (1997), 266-271. | MR | Zbl

[P] A. Polishchuk, On the Koszul property of the homogeneous coordinate ring of a curve, J. Algebra, 178, no. 1 (1995), 122-135. | DOI | MR | Zbl

[P2] A. Polishchuk, Koszul configurations of points in projective spaces. J. Algebra, 298, no. 1 (2006), 273-283. | DOI | MR | Zbl

[R] J. E. Roos, A description of the homological behaviour of families of quadratic forms in four variables, in Syzygies and Geometry, Boston 1995, A. Iarrobino, A. Martsinkovsky and J. Weyman eds., pp. 86-95, Northeastern Univ. 1995.

[RS] J. E. Roos - B. Sturmfels, A toric ring with irrational Poincaré-Betti series, C. R. Acad. Sci. Paris Sér. I Math., 326, no. 2 (1998), 141-146. | DOI | MR | Zbl

[S] J. Paris Serre, Algébre locale. Multiplicités, Lecture Notes in Mathematics 11, Springer, 1965. | MR

[VF] A. Vishik - M. Finkelberg, The coordinate ring of general curve of genus $g \geq 5$ is Koszul, J. Algebra, 162, no. 2 (1993), 535-539. | DOI | MR | Zbl