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Ideals with linear quotients in Segre products

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Języki publikacji
EN
Abstrakty
EN
We establish that the Segre product between a polynomial ring on a field K in m variables and the second squarefree Veronese subalgebra of a polynomial ring on K in n variables has the intersection degree equal to three. We describe a class of monomial ideals of the Segre product with linear quotients.
Słowa kluczowe
Rocznik
Strony
829--837
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • University of Reggio Calabria, DUES Via Graziella, Salita Feo di Vito Reggio Calabria, Italy
Bibliografia
  • [1] A. Aramova, J. Herzog, T. Hibi, Finite lattices and lexicographic Grobner bases, Europ. J. Combin. 21 (2000) 4, 431-439.
  • [2] A. Aramova, J. Herzog, T. Hibi, Finite lattices, lexicographic Grobner bases and sequentially Koszul algebras (unpublished).
  • [3] J. Backelin, R. Froeberg, Koszul algebras, Veronese subrings and rings with linear-resolution, Revue Roumaine Mathe. Pure Appl. 30 (1985) 2, 85-97.
  • [4] W. Bruns, J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, 1993.
  • [5] G. Failla, Protective Toric varietes and associated fibers, Rend. Circ. Mat. Palermo (2) Suppl. 77 (2006), 267-280.
  • [6] G. Failla, Binomial ideals and applications, Communications to Simai Congress 2 (2007).
  • [7] G. Failla, Quadratic Plucker relations for Hankel varieties, Rend. Circ. Mat. Palermo (2) Suppl. 81 (2009), 171-180.
  • [8] G. Failla, On certain Loci of Hankel r-planes o/Pm, Mathematical Notes 92 (2012) 4, 544-553.
  • [9] G. Failla, On the defining equations of the Hankel varieties H(2,n), Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 104 (2013), Tome 56, 403-418.
  • [10] G. Failla, On the (l,l)-Segre model for business, Applied Mathematical Sciences 8 (2014), 8329-8336.
  • [11] G. Failla, Combinatorics of Hankel relations, Ann. Acad. Rom. Sci. Ser. Math. Appl. 9 (2017) 2 (to appear).
  • [12] G. Failla, Linear triangulations of polytopes, Aplimat 2017, 16th Conference on Applied Mathematics, Proceedings (2017), 499-509.
  • [13] G. Failla, Ideals with linear resolution in Segre products, An. Univ. Craiova Ser. Mat. Inform. 44 (2017) 1, 149-155.
  • [14] G. Failla, R. Utano, Connected graphs arising from products of Veronese varieties, Algebra Colloq. 23 (2016), 281-292.
  • [15] G. Restuccia, G. Rinaldo, Intersection degree and bipartite graphs, ADJM 8 (2008) 2, 114-124.
  • [16] J. Herzog, T. Hibi, Componentwise linear ideals, Nagoya Math. J. 153 (1995), 141-153.
  • [17] J. Herzog, Y. Takayama, Resoultion by mapping cones, Homology Homotopy Appl. 4 (no. 2, part 2) (2002), 277-291.
  • [18] J. Herzog, T. Hibi, G. Restuccia, Strongly Koszul algebras, Math. Scand. 86 (2000), 161-178.
  • [19] L. Sherifan, M. Varbaro, Graded Betti numbers of ideals with linear quotients, Le Matematiche 63 (2008) 2, 257-265.
  • [20] B. Sturmfels, Grobner Bases and Convex Polytopes, Univ. Lect. Series 8, Amer. Math. Soc, 1995.
  • [21] R.H. Villarreal, Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics, vol. 238, Marcel and Dekker, Inc., New York, 2001.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
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Bibliografia
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bwmeta1.element.baztech-2ad97025-2892-4f28-8661-11101a0d9e7c
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