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Original Articles

Hilbert Series of Generic Ideals in Products of Projective Spaces

References

  • Anick, D. (1986). Thin algebras of embedding dimension three. J. Algebra. 100, 235–259. doi:10.1016/0021-8693(86)90076-1
  • Aubry, M. (1995). Série de Hilbert d’une algèbre de polynômes quotient. J. Algebra. 100, 235–259.
  • Backelin, J., Oneto, A. (2015). On a class of power ideals. J. Pure Appl. Algebra. 219, 3158–3180. doi:10.1016/j.jpaa.2014.10.007
  • Chandler, K. (2005). The geometric interpretation of the Fröberg-Iarrobino conjectures on infinitesimalneighbourhoods of points in projective space. J. Algebra. 286, 421–455. doi:10.1016/j.jalgebra.2005.01.010
  • Fröberg, R. (1985). An inequality for Hilbert series. Math. Scand. 56, 117–144. doi:10.7146/math.scand.a-12092
  • Fröberg, R., Gulliksen, T., Löfwall, C. (1983). Flat families of local artinian k-algebras with infinitely many Poincaré series. In: Roos, J.-E., ed. Springer Lect. Notes in Math., Vol. 1183. Berlin: Springer-Verlag, pp. 170–191.
  • Fröberg, R., Hollman, J. (1994). Hilbert series for ideals generated by generic forms. J. Symb. Comput. 17, 149–157. doi:10.1006/jsco.1994.1008
  • Fröberg, R., Lundqvist, S. (2018). Questions and conjectures on Extremal Hilbert series. Rev. Un. Mat. Argentina. 59(2), 415–429.
  • Fröberg, R., Löfwall, C. (1990). On Hilbert series for commutative and noncommutative graded algebras. J. Pure. Appl. Algebra. 76, 33–38. doi:10.1016/0022-4049(91)90095-J
  • Hochster, M., Laksov, D. (1987). The linear syzygies of generic forms. Comm. Algebra. 15, 227–234. doi:10.1080/00927872.1987.10487449
  • Iarrobino, A. (1997). Inverse systems of a symbolic power III. Thin algebras and fat points. Compositio Math. 108, 319–336.
  • Macaulay, F. (1927). Some properties of enumeration in the theory of modular systems. Proc. London Math. Soc. 26, 531–555. doi:10.1112/plms/s2-26.1.531
  • Migliore, J., Miro-Roig, R. M. (2003). Ideals of general forms and the ubiquity of the weak Lefschetz property. J. Pure Appl. Algebra. 102, 79–107. doi:10.1016/S0022-4049(02)00314-6
  • Nenashev, G. (2017). A note on Fröberg’s conjecture for forms of equal degree. C. R. Acad. Sci. Paris Ser. I, 355, 272–276. doi:10.1016/j.crma.2017.01.011
  • Nicklasson, L. (2017). On the Hilbert series of ideals generated by generic forms. Comm. Algebra. 45(8): 3390–3395. doi:10.1080/00927872.2016.1236931
  • Stanley, R. (1980). Weyl groups, the hard Lefschetz theorem, and the Sperner property. SIAM J. Algebraic Discrete Methods. 1, 168–184. doi:10.1137/0601021