Syzygies of Hibi Rings

Viviana Ene1,2
1Faculty of Mathematics and Computer Science, Ovidius University, Constanta, Romania
2Simion Stoilow Institute of Mathematics of the Romanian Academy, Research group of the project ID-PCE-2011-1023, Bucharest, Romania

Tóm tắt

We survey recent results on resolutions of Hibi rings.

Từ khóa


Tài liệu tham khảo

Aramova, A., Herzog, J., Hibi, T.: Finite lattices and lexicographic Gröbner bases. Eur. J. Comb 21, 431–439 (2000) Birkhoff, G.: Lattice Theory. 3rd ed, vol. 25. RI, Providence (1967) Björner, A., Garsia, A., Stanley, R. An introduction to the theory of Cohen-Macaulay partially ordered sets. In: Rival, I. (ed.) : Ordered Sets, pp 583–615. Reidel, Dordrecht/Boston/London (1982) Bruns, W., Herzog, J.: Cohen-Macaulay Rings. Cambridge University Press, Revised Ed. (1998) Bruns, W., Herzog, J.: Semigroup rings and simplicial complexes. J. Pure Appl. Algebra 122, 185–208 (1997) Eisenbud, D.: Introduction to algebras with straightening laws. In: “Ring theory and algebra”, III: Proceedings of the third Oklahoma Conference, vol. 55, pp 243–268. Lecture Notes in Pure and Applied Mathematics (1980) Eisenbud, D.: Commutative algebra with a view toward algebraic geometry. Grad Texts in Math, vol. 150. Springer, Berlin (1995) Ene, V., Herzog, J.: Gröbner bases in commutative algebra. Grad. Stud. Math., vol. 130. Am. Math. Soc., Providence (2012) Ene, V., Herzog, J., Hibi, T.: Linear flags and Koszul filtrations. to appear in Kyoto J. Math. Ene, V., Herzog, J., Hibi, T.: Linearly related polyominoes. preprint. arXiv: 1403.4349 Ene, V., Herzog, J., Hibi, T., Saeedi Madani, S.: Pseudo-Gorenstein and level Hibi rings. arXiv:1405.6963 Ene, V., Herzog, J., Saeedi Madani, S.: A note on the regularity of Hibi rings. arXiv:2554.1404 Ene, V., Herzog, J., Mohammadi, F.: Monomial ideals and toric rings of Hibi type arising from a finite poset. Eur. J. Comb. 32, 404–421 (2011) Ene, V., Hibi, T.: The join-meet ideal of a finite lattice. J. Commut. Algebra 5(2), 209–230 (2013) Ene, V., Qureshi, A.A., Rauf, A.: Regularity of join-meet ideals of distributive lattices. Electron. J. Combin. 20(3), 20 (2013) Hashimoto, M., Hibi, T., Noma, A.: Divisor class groups of affine semigroup rings associated with distributive lattices. J. Algebra 149, 352–357 (1992) Herzog, J. Finite free resolutions. In: Cojocaru, S., Pfister, G. , Ufnrovschi, V. (eds.) : Computational Commutative and Non-Commutative Algebraic Geometry. NATO Science Series, Series III: Computer and System Sciences-vol. 196, pp. 118–145 (2005). IOS Press Herzog, J., Hibi, T.: Monomial ideals. Grad Texts in Math, vol. 260. Springer, Berlin (2010) Herzog, J., Hibi, T.: Finite lattices and Gröbner bases. Math. Nachr. 285, 1969–1973 (2012) Herzog, J., Hibi, T., Restuccia, G.: Strongly Koszul algebras. Math. Scand. 86(2), 161–178 (2000) Herzog, J., Srinivasan, H.: A note on the subadditivity problem for maximal shifts in free resolutions. to appear in MSRI Proc. arXiv: 1303.6214 Hibi, T. Distributive lattices, affine semigroup rings and algebras with straightening laws. In: Nagata, M., Matsumura, H. (eds.) : Commutative Algebra and Combinatorics, vol. 11, pp 93–109. Adv. Stud. Pure Math, North–Holland, Amsterdam (1987) Hibi, T.: Level rings and algebras with straightening laws. J. Algebra 117, 343–362 (1988) Hochster, M.: Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes. Ann. of Math. 96(2), 318–337 (1972) Kumar, C., Singh, P., Kumar, A.: Nearly extremal Cohen-Macaulay and Gorenstein algebras. Bull. Austral. Math. Soc. 75, 211–220 (2007) Miyazaki, M.: A sufficient condition for a Hibi ring to be level and levelness of Schubert cycles. Comm. Algebra 35, 2894–2900 (2007) Peeva, I.: Graded syzygies. Algebr Appl., vol. 14. Springer, New York (2011) Qureshi, A.: Ideals generated by 2-minors, collections of cells and stack polyominoes. J. Algebra 357, 279–303 (2012) Qureshi, A.: Indispensable Hibi relations and Gröbner bases. to appear in Algebra Colloq. Sally, J.: Cohen-Macaulay rings of maximal embedding dimension. J. Algebra 56, 168–183 (1979) Schenzel, P.: Uber die freien Auflösungen extremaler Cohen-Macaulay Ringe. J. Algebra 64, 93–101 (1980) Stanley, R.P. Cohen-Macaulay Complexes. In: Aigner, M. (ed.) : Higher Combinatorics. NATO Advanced Study Institute Series, pp 51–62. Reidel, Dordrecht/Boston (1977) Stanley, R.P.: Hilbert functions of graded algebras. Adv. Math. 28, 57–83 (1978) Stanley, R.P.: Combinatorics and Commutative Algebra. Progress in Mathematics. 2nd edition, vol. 41. Birkhäuser, Boston/Basel/Stuttgart (1996) Stanley, R.P.: Enumerative combinatorics. 2nd ed, vol. 1. Cambridge University Press, Cambridge (1996) Wagner, D.G.: Singularities of toric varieties associated with finite distributive lattices. J. Algebraic Combin. 5, 149–165 (1996)