On the Lefschetz property for quotients by monomial ideals containing squares of variables

References

• Adiprasito, K., Papadakis, S. A., Petrotou, V. (2021). Anisotropy, biased pairings, and the Lefschetz property for pseudomanifolds and cycles. Preprint.
   Google Scholar
• Altafi, N., Boij, M. (2020). The weak Lefschetz property of equigenerated monomial ideals. J. Algebra 556:136–168. DOI: 10.1016/j.jalgebra.2020.02.020.
   Web of Science ®Google Scholar
• Blekherman, G., Sinn, R., Velasco, M. (2017). Do sums of squares dream of free resolutions?. SIAM J. Appl. Algebra Geom. 1:175–199. DOI: 10.1137/16M1084560.
   Web of Science ®Google Scholar
• Brenner, H., Kaid, A. (2007). Syzygy bundles on P2 and the weak Lefschetz property. Illinois J. Math. 51:1299–1308.
   Google Scholar
• Cook, D., Nagel, U. (2016). The weak Lefschetz property for monomial ideals of small type. J. Algebra 462:285–319. DOI: 10.1016/j.jalgebra.2016.06.004.
   Web of Science ®Google Scholar
• D’Alí, A., Venturello, L. (2023). Koszul Gorenstein algebras from Cohen-Macaulay simplicial complexes. Int. Math. Res. Not. 2023(6):4998–5045. DOI: 10.1093/imrn/rnac003.
   Web of Science ®Google Scholar
• Eisenbud, D., Huneke, C., Ulrich, B. (2006). The regularity of Tor and graded Betti numbers. Amer. J. Math. 128:573–605. DOI: 10.1353/ajm.2006.0022.
   Web of Science ®Google Scholar
• Godsil, C., Royle, G. (2001). Algebraic Graph Theory. New York: Springer-Verlag, p. 166.
   Google Scholar
• Gondim, R., Zappalà, G. (2018). Lefschetz properties for Artinian Gorenstein algebras presented by quadrics. Proc. Amer. Math. Soc. 146(3):993–1003. DOI: 10.1090/proc/13822.
   Web of Science ®Google Scholar
• Harima, T., Maeno, T., Morita, H., Numata, Y., Wachi, A., Watanabe, J. (2013). The Lefschetz Properties. Springer Lecture Notes in Mathematics, Vol. 2080. Heidelberg: Springer.
   Google Scholar
• Hertrich, C., Schröder, F., Steiner, R. (2020). Coloring drawings of graphs. Preprint.
   Google Scholar
• Iarrobino, A., McDaniel, C., Seceleanu, A. (2022). Connected sums of graded Artinian Gorenstein algebras and Lefschetz properties. J. Pure Appl. Algebra 226(1):106787. DOI: 10.1016/j.jpaa.2021.106787.
   Web of Science ®Google Scholar
• Kubitzke, M., Nevo, E. (2009). The Lefschetz property for barycentric subdivisions of shellable complexes. Trans. Amer. Math. Soc. 361:6151–6163. DOI: 10.1090/S0002-9947-09-04794-1.
   Web of Science ®Google Scholar
• Lawrencenko, S., Vyalyi, M. N., Zgonnik, L. V. (2017). Grünbaum coloring and its generalization to arbitrary dimension. Australas. J. Combin. 67(2):119–130.
   Google Scholar
• Liu, W., Lawrencenko, S., Chen, B., Ellingham, M. N., Hartsfield, N., Yang, H., Ye, D., Zha, X. (2019). Quadrangular embeddings of complete graphs and the Even Map Color theorem. J. Combin. Theory Ser. B 139(1):1–26. DOI: 10.1016/j.jctb.2019.02.006.
   Google Scholar
• Mastroeni, M., Schenck, H., Stillman, M. (2021). Quadratic Gorenstein rings and the Koszul property I. Trans. Amer. Math. Soc. 374(2):1077–1093. DOI: 10.1090/tran/8214.
   Web of Science ®Google Scholar
• Mermin, J., Peeva, I., Stillman, M. (2008). Ideals containing the squares of the variables. Adv. Math. 217(5):2206–2230. DOI: 10.1016/j.aim.2007.11.014.
   Web of Science ®Google Scholar
• Mezzetti, E., Miró-Roig, R., Ottaviani, G. (2013). Laplace equations and the weak Lefschetz property. Can. J. Math. 65(3):634–654. DOI: 10.4153/CJM-2012-033-x.
   Web of Science ®Google Scholar
• Michalek, M., Miró-Roig, R. (2016). Smooth monomial Togliatti systems of cubics. J. Combin. Theory Ser. A 143:66–87. DOI: 10.1016/j.jcta.2016.05.004.
   Web of Science ®Google Scholar
• Migliore, J., Miró-Roig, R., Nagel, U. (2011). Monomial ideals, almost complete intersections and the Weak Lefschetz property. Trans. Amer. Math. Soc. 363:229–257. DOI: 10.1090/S0002-9947-2010-05127-X.
   Web of Science ®Google Scholar
• Migliore, J., Nagel, U. (2013). A tour Of the weak and strong Lefschetz properties. J. Commut. Algebra 5:329–358. DOI: 10.1216/JCA-2013-5-3-329.
   Web of Science ®Google Scholar
• Migliore, J., Nagel, U., Schenck, H. (2020). The weak Lefschetz property for quotients by quadratic monomials. Math. Scand. 126:41–60. DOI: 10.7146/math.scand.a-116681.
   Web of Science ®Google Scholar
• McCullough, J., Seceleanu, A. (2020). Quadratic Gorenstein algebras with many surprising properties. Arch. Math. (Basel) 115(5):509–521. DOI: 10.1007/s00013-020-01492-x.
   Web of Science ®Google Scholar
• Stanley, R. P. (1980). Weyl groups, the hard Lefschetz theorem, and the Sperner property. SIAM J. Algebraic Discrete Methods 1:168–184. DOI: 10.1137/0601021.
   Web of Science ®Google Scholar
• Stanley, R. P. (1983). Combinatorial applications of the Hard Lefschetz theorem. In: Proceedings of the International Congress of Mathematicians Warsaw (1983), pp. 447–453.
   Google Scholar