Specializations of Ferrers ideals
Alberto Corso
and Uwe Nagel
University of Kentucky Department of Mathematics Lexington KY 40506 USA
DOI: 10.1007/s10801-007-0111-2
Abstract
We introduce a specialization technique in order to study monomial ideals that are generated in degree two by using our earlier results about Ferrers ideals. It allows us to describe explicitly a cellular minimal free resolution of various ideals including any strongly stable and any squarefree strongly stable ideal whose minimal generators have degree two. In particular, this shows that threshold graphs can be obtained as specializations of Ferrers graphs, which explains their similar properties.
Pages: 425–437
Keywords: keywords ferrers graphs; threshold graphs; monomial (edge) ideals; cellular minimal free resolution
Full Text: PDF
References
1. Aramova, A., Herzog, J., Hibi, T.: Squarefree lexsegment ideals. Math. Z. 228, 353-378 (1998)
2. Bayer, D., Sturmfels, B.: Cellular resolutions of monomial modules. J. Reine Angew. Math. 502, 123-140 (1998)
3. Bayer, D., Peeva, I., Sturmfels, B.: Monomial resolutions. Math. Res. Lett. 5, 31-46 (1998)
4. Corso, A., Nagel, U.: Monomial and toric ideals associated to Ferrers graphs. Trans. Am. Math. Soc. (2007, to appear)
5. Eisenbud, D., Green, M., Hulek, K., Popescu, S.: Small schemes and varieties of minimal degree. Am. J. Math. 128, 1363-1389 (2006)
6. Eliahou, S., Kervaire, M.: Minimal resolutions of some monomial ideals. J. Algebra 129, 1-25 (1990)
7. Horwitz, N.: Linear resolutions of quadratic monomial ideals. J. Algebra 318, 981-1001 (2007)
8. Klivans, C., Reiner, V.: Shifted set families, degree sequences, and plethysm. Electron. J. Comb.
2. Bayer, D., Sturmfels, B.: Cellular resolutions of monomial modules. J. Reine Angew. Math. 502, 123-140 (1998)
3. Bayer, D., Peeva, I., Sturmfels, B.: Monomial resolutions. Math. Res. Lett. 5, 31-46 (1998)
4. Corso, A., Nagel, U.: Monomial and toric ideals associated to Ferrers graphs. Trans. Am. Math. Soc. (2007, to appear)
5. Eisenbud, D., Green, M., Hulek, K., Popescu, S.: Small schemes and varieties of minimal degree. Am. J. Math. 128, 1363-1389 (2006)
6. Eliahou, S., Kervaire, M.: Minimal resolutions of some monomial ideals. J. Algebra 129, 1-25 (1990)
7. Horwitz, N.: Linear resolutions of quadratic monomial ideals. J. Algebra 318, 981-1001 (2007)
8. Klivans, C., Reiner, V.: Shifted set families, degree sequences, and plethysm. Electron. J. Comb.