Arithmetical rank of squarefree monomial ideals of small arithmetic degree

Springer Science and Business Media LLC - Tập 29 Số 3 - Trang 389-404 - 2009
Kohei Kimura1, Naoki Terai2, Ken-ichi Yoshida1
1Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan
2Department of Mathematics, Faculty of Culture and Education, Saga University, Saga, 840-8502, Japan

Tóm tắt

Từ khóa


Tài liệu tham khảo

Barile, M.: On the number of equations defining certain varieties. Manuscripta Math. 91, 483–494 (1996)

Barile, M.: A note on monomial ideals. Arch. Math. 87, 516–521 (2006)

Barile, M.: A note on the edge ideals of Ferrers graphs. Preprint, math.AC/0606353

Barile, M.: On the arithmetical rank of the edge ideals of forests. Preprint, math.AC/0607306

Barile, M.: On the arithmetical rank of certain monomial ideals. Preprint, math.AC/0611790

Barile, M.: Arithmetical ranks of Stanley–Reisner ideals via linear algebra. Preprint, math.AC/0703258

Frühbis-Krüger, A., Terai, N.: Bounds for the regularity of monomial ideals. Matematiche (Catania) 53, 83–97 (1998)

Hoa, L.T., Trung, N.V.: On the Castelnuovo–Mumford regularity and the arithmetic degree of monomial ideals. Math. Z. 229, 519–537 (1998)

Lyubeznik, G.: On the local cohomology modules $H^{i}_{\mathfrak{a}}(R)$ for ideals $\mathfrak{a}$ generated by monomials in an R-sequence. In: Greco, S., Strano, R. (eds.) Complete Intersections, Acireale, 1983. Lecture Notes in Mathematics, vol. 1092, pp. 214–220. Springer, Berlin (1984)

Schenzel, P.: Applications of Koszul homology to numbers of generators and syzygies. J. Pure Appl. Algebra 114, 287–303 (1997)

Schenzel, P., Vogel, W.: On set-theoretic intersections. J. Algebra 48, 401–408 (1977)

Schmitt, T., Vogel, W.: Note on set-theoretic intersections of subvarieties of projective space. Math. Ann. 245, 247–253 (1979)

Stückrad, J., Vogel, W.: Buchsbaum Rings and Applications. Springer, Berlin (1986)

Terai, N.: Alexander duality in Stanley–Reisner rings. In: Hibi (ed.) Affine Algebraic Geometry, in Honor of Professor Masayoshi Miyanishi on the Occasion of His Retirement from Osaka University, pp. 449–462. Osaka University Press (2007)

Yan, Z.: An étale analog of the Goresky–Macpherson formula for subspace arrangements. J. Pure Appl. Algebra 146, 305–318 (2000)