Bounds on the regularity and projective dimension of ideals associated to graphs
Tóm tắt
Từ khóa
Tài liệu tham khảo
Chudnovsky, M., Seymour, P.: The structure of claw-free graphs. In: Surveys in Combinatorics. London Math. Soc. Lecture Note Ser., vol. 327, pp. 153–171. Cambridge University Press, Cambridge (2005)
Dao, H. ( mathoverflow.net/users/2083 ): How to construct log-canonical (or Calabi–Yau) non-Cohen–Macaulay singularities of low codimensions? http://mathoverflow.net/questions/69436 (version: 2011-07-06)
Dao, H., Schweig, J.: Projective dimension, graph domination parameters, and independence complex homology. Preprint, 1110.2841
Dochtermann, A., Engström, A.: Algebraic properties of edge ideals via combinatorial topology. Electron. J. Combin. 16 (2009). Special volume in honor of Anders Björner, Research Paper 2
Eisenbud, D.: Commutative Algebra. With a View Toward Algebraic Geometry. Graduate Texts in Mathematics, vol. 150. Springer, New York (1995)
Eisenbud, D., Mustata, M., Stillman, M.: Cohomology on toric varieties and local cohomology with monomial supports. J. Symb. Comput. 29, 583–600 (2000)
Eisenbud, D., Green, M., Hulek, K., Popescu, S.: Restricting linear syzygies: algebra and geometry. Compos. Math. 141, 1460–1478 (2005)
Faltings, G.: Über lokale Kohomologiegruppen hoher Ordnung. J. Reine Angew. Math. 313, 43–51 (1980)
Francisco, C., Van Tuyl, A.: Sequentially Cohen–Macaulay edge ideals. Proc. Am. Math. Soc. 135, 2327–2337 (2007)
Goff, M.: Simplicial girth and pure resolutions. Graphs Comb. (2011). doi: 10.1007/s00373-011-1113-3
Goodarzia, A., Pournakib, M.R., Seyed Fakharib, S.A., Yassemi, S.: On the h-vector of a simplicial complex with Serre’s condition. J. Pure Appl. Algebra 216, 91–94 (2012)
Há, H.T., Van Tuyl, A.: Splittable ideals and the resolutions of monomial ideals. J. Algebra 309, 405–425 (2007)
Há, H.T., Van Tuyl, A.: Resolution of square-free monomial ideals via facet ideals: a survey. Contemp. Math. 448, 91–117 (2007)
Huneke, C., Lyubeznik, G.: On the vanishing of local cohomology modules. Invent. Math. 102, 73–93 (1990)
Kummini, M.: Homological invariants of monomial and binomial ideals. Thesis, University of Kansas (2008)
Kummini, M.: Regularity, depth and arithmetic rank of bipartite edge ideals. J. Algebr. Comb. 30, 429–445 (2009)
Lyubeznik, G.: The minimal non-Cohen–Macaulay monomial ideals. J. Pure Appl. Algebra 51, 261–266 (1988)
Mayr, E., Meyer, A.: The complexity of the word problems for commutative semigroups and polynomial ideals. Adv. Math. 46, 305–329 (1982)
McCullough, J.: A polynomial bound on the regularity of an ideal in terms of half of the syzygies. Preprint, 1112.0058
Miller, E., Sturmfels, B.: Combinatorial Commutative Algebra. Graduate Texts in Mathematics, vol. 227. Springer, New York (2005)
Miyazaki, M.: On the discrete counterparts of algebras with straightening laws. J. Commut. Algebra 2, 79–89 (2010)
Morey, S., Villarreal, R.: Edge ideals: algebraic and combinatorial properties. In: Progress in Commutative Algebra, Combinatorics and Homology, vol. 1, pp. 85–126 (2012)
Murai, S., Terai, T.: H-vectors of simplicial complexes with Serre’s conditions. Math. Res. Lett. 16, 1015–1028 (2009)
Nevo, E.: Regularity of edge ideals of C 4-free graphs via the topology of the lcm-lattice. J. Comb. Theory, Ser. A 118, 491–501 (2011)
Nevo, E., Peeva, I.: Linear resolutions of powers of edge ideals. Preprint
Norin, S. ( mathoverflow.net/users/8733 ): Upper bounds on number of vertices of graphs whose complements have no induced cycles of certain lengths. http://mathoverflow.net/questions/66112 (version: 2011-05-28)
Ogus, A.: Local cohomological dimension of algebraic varieties. Ann. Math. 98, 999–1013 (1976)
Peskine, C., Szpiro, L.: Dimension projective finie et cohomologie locale. Publ. Math. IHÉS 42, 47–119 (1973)
Singh, A., Walther, U.: Local cohomology and pure morphisms. Ill. J. Math. 51, 287–298 (2007). Special Issue in Honor of Phil Griffith
Terai, N.: Alexander duality theorem and Stanley–Reisner rings. In: Free Resolution of Defining Ideals of Projective Varieties (Japanese), Kyoto, 1998. Surikaisekikenkyusho Kokyuroku, vol. 1078, pp. 174–184 (1999)
Varbaro, M.: Gröbner deformations, connectedness and cohomological dimension. J. Algebra 322, 2492–2507 (2009)
Whieldon, G.: Jump sequences of edge ideals. arXiv:1012.0108