g-Elements of matroid complexes

@article{Swartz2003gElementsOM,
  title={g-Elements of matroid complexes},
  author={Ed Swartz},
  journal={J. Comb. Theory, Ser. B},
  year={2003},
  volume={88},
  pages={369-375}
}
A g-element for a graded R-module is a one-form with properties similar to a Lefschetz class in the cohomology ring of a compact complex projective manifold, except that the induced multiplication maps are injections instead of bijections. We show that if k(∆) is the face ring of the independence complex of a matroid and the characteristic of k is zero, then there is a non-empty Zariski open subset of pairs (Θ, ω) such that Θ is a linear set of paramenters for k(∆) and ω is a g-element for k… CONTINUE READING

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